Mechanics Questions

An athlete in the olympic games covers a distance of $100\text{m}$ in $10\text{s}$. His kinetic energy can be estimated to be in the range:

A $20\text{ cm}$ long capillary tube is dipped in water. The water rises up to $8\text{ cm}$. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be:

Identify the vector quantity from the following:

The momentum of a particle having mass $m$ is $p$. Its kinetic energy will be

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would:

If $S$ is stress and $Y$ is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is:

Consider a uniform square plate of side ‘$a$ ’ and mass ‘$m$ ’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is:

Two simple harmonic motions are represented by the equation $y_1=0.1\sin (100\pi t+\pi /3)$ and $y_2=0.1\cos \pi t$. The phase difference of the velocity of particle $1$ w.r.t. the velocity of the particle $2$ is:

A particle of mass $0.3\text{ kg}$ is subjected to a force $F=-kx$ with $k=15\text{ N/m}$. What will be its initial acceleration if it is released from a point $20\text{ cm}$ away from the origin?

A body of mass $m=3.513\text{kg}$ is moving along the $x$ -axis with a speed of $5.00\text{m/s}$. The magnitude of its momentum is recorded as:

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function time is given by:

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is:

A small particle of mass $m$ is projected at an angle $\theta$ with the $x$ -axis with an initial velocity $v_0$ in the $x-y$ plane. At a time $t<\frac{v_0\sin \theta }{g}$, the angular momentum of the particle about the origin is:

A bomb is released from a moving aeroplane flying horizontally at a uniform speed. Neglecting air resistance, what path does the bomb appear to follow according to the pilot?

A body is acted upon by two unequal forces in opposite directions, but not in one line. The effect is that the body will have:

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is:

A thin rod of length $L$ is lying along the $x$ -axis from $x=0$ to $x=L$. Its linear density $\lambda$ varies as $\lambda =k(x/L{)}^n$. Which graph best approximates the dependence of the position $x_{CM}$ of the centre of mass on $n$ ($n\ge 0$)?

A rocket with a lift-off mass $3.5\times 10^4\text{kg}$ is blasted upwards with an initial acceleration of $10{\text{m/s}}^2$. Then the initial thrust of the blast is:

A wire suspended vertically from one of its ends stretched by attaching weight of $200\text{N}$ to the lower end. The weight stretches the wire by $1\text{mm}$. Then the elastic energy stored in the wire is:

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau }$ be the torque of this force about the origin. Then:

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M\text{kg}$ hangs from the former one. Then the true statement about scale reading is:

Rate of work done is ________.

What is the unit of the physical quantity "Young's modulus"?

A person on a swing stands up. The time period of the swing:

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be:

Law of gravitation applies to __________.

A body A of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3M$ and a body C of mass $2/3M$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards:

Consider the following two statements:(1) Linear momentum of a system of particles is zero.(2) Kinetic energy of system of particles is zero.

A particle executes linear simple harmonic motion with an amplitude of $3\text{cm}$. When the particle is at $2\text{cm}$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

The co-ordinates of a moving particle at any time $t$ are given by $x=\alpha t^3$ and $y=\beta t^3$. The speed of the particle at time $t$ is given by:

A block of mass $M$ is pulled along a horizontal friction surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block is:

A marble block of mass $2\text{kg}$ lying on ice when given a velocity of $6\text{m/s}$ is stopped by friction in $10\text{s}$. The coefficient of friction is:

The $x$ and $y$ coordinates of the particle at any time are $x=5t-2t^2$ and $y=10t$ respectively, where $x$ and $y$ are in meters and $t$ in seconds. The acceleration of the particle at $t=2\text{s}$ is:

Two blocks $A$ and $B$ of masses $3m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively:

In the equation of motion 2as=v
2
−u
2
, s represents _______.

Which one of the following statements is incorrect?

A body starts from rest at $x=0,t=0$ with constant acceleration $a$. Simultaneously another body passes $x=0$ with constant speed $v$. The position of the first is $x_1(t)$ and the second is $x_2(t)$. Which graph describes $(x_1-x_2)$ vs $t$?

A boy playing on the roof of a $10\text{m}$ high building throws a ball with a speed of $10\text{m/s}$ at an angle of $30^{\circ }$ with the horizontal. How far from the throwing point will the ball be at the height of $10\text{m}$ from the ground? (Take $g=10{\text{m/s}}^2$)

Three forces start acting simultaneously on a particle moving with velocity $\vec{v}$. These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ taken in order. The particle will now move with velocity:

A car moving with a speed of $50\text{km/hr}$, can be stopped by brakes after at least $6\text{m}$. If the same car is moving at a speed of $100\text{km/hr}$, the minimum stopping distance is:

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $u$ and the other from rest with uniform acceleration $f$. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time:

A spring of spring constant $5\times 10^3\text{N/m}$ is stretched initially by $5\text{cm}$ from the unstretched position. Then the work required to stretch it further by another $5\text{cm}$ is:

A horizontal force of $10\text{N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is:

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49\text{N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5{\text{m/s}}^2$, the reading of the spring balance will be:

Two stones are projected from the top of a cliff $h$ meters high, with the same speed $u$ so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle $\theta$ to the horizontal then $\tan \theta$ equals:

A couple is of moment $\vec{G}$ and the force forming the couple is $\vec{P}$. If $\vec{P}$ is turned through a right angle, the moment of the couple thus formed is $\vec{H}$. If instead, the forces $\vec{P}$ are turned through an angle $\alpha$, then the moment of couple becomes:

A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration $f$ and in the second part with constant retardation $r$. The value of $t$ is given by:

A spherical ball of mass $20\text{ kg}$ is stationary at the top of a hill of height $100\text{ m}$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30\text{ m}$ and finally rolls down to a horizontal base at a height of $20\text{ m}$ above the ground. The velocity attained by the ball is:

The change in the value of $g$ at a height ‘$h$ ’ above the surface of the earth is the same as at a depth ‘$d$ ’ below the surface of earth. When both ‘$d$ ’ and ‘$h$ ’ are much smaller than the radius of earth, then which one of the following is correct?

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to:

The resultant of forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled then $\vec{R}$ is doubled. If the direction of $\vec{Q}$ is reversed, then $\vec{R}$ is again doubled. Then $P^2:Q^2:R^2$ is:

A bullet fired into a fixed target loses half of its velocity after penetrating $3\text{ cm}$. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A ball of mass $0.15\text{kg}$ is dropped from a height $10\text{m}$, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g=10{\text{m/s}}^2$) nearly:

A smooth block is released at rest on a $45^{\circ }$ incline and then slides a distance $d$. The time taken to slide is $n$ times as much to slide on a rough incline than on a smooth incline. The coefficient of friction is:

A particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively:

A shaving brush is dipped in water. When taken out, the hairs of the brush are seen to be drawn tightly together due to the:

A car starts from rest and accelerates at $5{\text{m/s}}^2$. At $t=4\text{s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6\text{s}$? ($g=10{\text{m/s}}^2$)

The weight of an object of mass 1kg is approximately equal to ____ newton.

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is:

A body is acted upon by two unequal forces acting in opposite directions, but not along the same straight line. The effect is that the body will experience:

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\text{s}$. In another $10\text{s}$ it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals:

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is:

The unit of energy in MKS system is:

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to:

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity $v_1$ while body B is at rest before collision. The velocity of the system after collision is $v_2$. The ratio $v_1:v_2$ is:

Statement – I : A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f(\frac{1}{2}m{v}^2)$, then $f=\frac{m}{M+m}$.Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A spherical solid ball of volume $V$ is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_2$ (${\rho }_2<{\rho }_1$). Assume that the liquid applies a viscous force $F_{\text{viscous}}=-k{v}^2$. The terminal speed of the ball is:

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \text{rpm}$. The tension in the string is $T$. If speed becomes $2\omega$ while keeping the same radius, the tension in the string becomes:

A hoop of radius $r$ and mass $m$ rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

A thin flat circular disc of radius $4.5\text{cm}$ is placed gently over the surface of water. If surface tension of water is $0.07{\text{N m}}^{-1}$, then the excess force required to take it away from the surface is:

Let $[{ϵ}_0]$ denote the dimensional formula of the permittivity of vacuum. If $M=\text{mass},L=\text{length},T=\text{time}$ and $A=\text{electric current}$, then:

The maximum elongation of a steel wire of $1\text{m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8\times 10^8{\text{N m}}^{-2}$ and $2\times 10^{11}{\text{N m}}^{-2}$ is:

A wooden wheel of radius $R$ is made of two semicircular parts. The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is:

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $v$ in the direction shown, which one of the following options is correct ($P$ and $Q$ are any highest and lowest points on the wheel, respectively)?

A sonometer wire of length $1.5\text{m}$ is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times 10^3{\text{kg/m}}^3$ and $2.2\times 10^{11}{\text{N/m}}^2$ respectively?

Average density of the earth:

Two fixed frictionless inclined planes making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=[U(x=\infty )-U_{atequilibrium}]$, $D$ is:

A mass ‘$m$ ’ moves with a velocity $v$ and collides inelastically with another identical mass. After collision the 1st mass moves with velocity $v/\sqrt{3}$ in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision:

Consider a car moving on a straight road with a speed of $100\text{ m/s}$. The distance at which car can be stopped is [${\mu }_k=0.5$ ]:

If $S=ut+\frac{1}{2}a{t}^2$ and $u=50$, $a=9.8$, $t=2$, then the value of $S$ is:

A jar is filled with two non-mixing liquids $1$ and $2$ having densities ${\rho }_1$ and ${\rho }_2$ respectively. A solid ball of density ${\rho }_3$ is dropped and comes to equilibrium such that it floats at the interface, partially in both liquids. Which of the following is true for ${\rho }_1$, ${\rho }_2$ and ${\rho }_3$?

Let $R_1$ and $R_2$ respectively be the maximum ranges up and down an inclined plane and $R$ be the maximum range on the horizontal plane. Then $R_1,R,R_2$ are in:

Which physical unit is obtained by the ratio of momentum and velocity of matter?

Momentum of a particle of mass $m$ is $p$. Its kinetic energy will be

If $P$, $F$ and $A$ represent pressure, force and area respectively, then

If P, F and A represent pressure, force and area respectively, then the correct relationship is:

A bob of heavy mass $m$ is suspended by a light string of length $l$. The bob is given a horizontal velocity $v_0$ as shown in figure. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the speed $v$ of the bob at point $P$ to its initial speed $v_0$ is:

There are two inclined surfaces of equal length ($L$) and same angle of inclination $45^{\circ }$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (${\mu }_k$) between the object and the rough surface is close to:

A ball of mass $0.5\text{kg}$ is dropped from a height of $40\text{m}$. The ball hits the ground and rises to a height of $10\text{m}$. The impulse imparted to the ball during its collision with the ground is (Take $g=9.8{\text{m/s}}^2$):

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one half of its maximum height. How high does the ball rise ?

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms^-1. The kinetic energy of the other mass is :

A force F acting on an object varies with distance x as shown here. The force is in N and x is in m. The work done by the force in moving the object from x = 0 to x = 6 m is :

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone ?

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force :

Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is :

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is :

The circular motion of a particle with constant speed is :

The displacement x of a particle varies with time t as x = ae^(-αt) + be^(βt), where a, b, α and β are positive constants. The velocity of the particle will :