Mechanics Questions

A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body $A$ is:

A disc of radius $2\text{m}$ and mass $100\text{kg}$ rolls on a horizontal floor. Its centre of mass has speed of $20\text{cm/s}$. How much work is needed to stop it?

The displacement of a particle executing simple harmonic motion is given by $y=A_0+A\sin \omega t+B\cos \omega t$. Then the amplitude of its oscillation is given by:

A body weighs $200\text{N}$ on the surface of the earth. How much will it weigh half way down to the centre of the earth?

Average velocity of a particle executing SHM in one complete vibration is:

A solid cylinder of mass $2\text{kg}$ and radius $4\text{cm}$ rotating about its axis at the rate of $3\text{rpm}$. The torque required to stop after $2\pi$ revolutions is:

A force $F=20+10y$ acts on a particle in $y$ -direction where $F$ is in newton and $y$ in meter. Work done by this force to move the particle from $y=0$ to $y=1\text{m}$ is:

The work done to raise a mass $m$ from the surface of the earth to a height $h$, which is equal to the radius of the earth, is:

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ }$ with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to $30^{\circ }$ and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be:

The speed of a swimmer in still water is $20\text{m/s}$. The speed of river water is $10\text{m/s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by:

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will:

Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speed $v_A$ and $v_B$ respectively. Their time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be:

A block of mass $10\text{kg}$ is in contact against the inner wall of a hollow cylindrical drum of radius $1\text{m}$. The coefficient of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ($g=10{\text{m/s}}^2$)

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig. $y$ -projection of the radius vector of rotating particle $P$ is:

In an experiment, the percentage of error occurred in the measurement of physical quantities $A,B,C$ and $D$ are $1\%,2\%,3\%$ and $4\%$ respectively. Then the maximum percentage of error in the measurement $X$, where $X=\frac{A^2{B}^{1/2}}{C^{1/3}{D}^3}$, will be: