AIEEE 2011 PYQ Mock Test

Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega$ along the $x$ -axis. Their mean position is separated by distance $X_0$ ($X_0>A$). If the maximum separation between them is $(X_0+A)$, the phase difference between their motion is:

Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d$ ($d\ll l$) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity $v$. Then as a function of distance $x$ between them:

A boat is moving due east in a region where the earth's magnetic field is $5.0\times 10^{-5}{\text{NA}}^{-1}{\text{m}}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2\text{m}$ long. If the speed of the boat is $1.50{\text{ms}}^{-1}$, the magnitude of the induced emf in the wire of aerial is:

An object, moving with a speed of $6.25\text{m/s}$, is decelerated at a rate given by:
$$\frac{dv}{dt}=-2.5\sqrt{v}$$
where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be: