NEET UG 2003 — Mechanics

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time?

The acceleration due to gravity on the planet $\mathrm{A}$ is 9 times the acceleration due to gravity on planet B. A man jumps to a height of $2 \mathrm{~m}$ on the surface of A. What is the height of jump by the same person on the plane $\mathrm{B}$ ?

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is $K$. If radius of the ball be $R$, then the fraction of total energy associated with its rotational energy will be:

When a long spring is stretched by $2 \mathrm{~cm}$, its potential energy is $U$. If the spring is stretched by $10 \mathrm{~cm}$, the potential energy stored it will be:

A thin circular ring of Mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity 3 . The gravitational force will now be:

A monkey of mass $20 \mathrm{~kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \mathrm{~kg}$ is suspended from it but will break if the mass exceeds $25 \mathrm{~kg}$. What is the maximum acceleration with which monkey can climb up along the rope?

The vector sum of two forces is perpendicular to their vector differences. In that case, the force:

A man weighs $80 \mathrm{~kg}$. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $5 \mathrm{~m} / \mathrm{s}^2$. What would be the reading on the scale? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

If a ball is thrown vertically with speed $u$, the distance covered during the last $t$ seconds of its ascent is:

A solid cylinder of mass $M$ and radius $R$ rolls without slipping on an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom?

A particle moves along a circle $\left(\frac{20}{\pi}\right) \mathrm{m}$ with constant tangential acceleration. If the velocity of the particle is $80 \mathrm{~m} / \mathrm{s}$ at the end of the second revolution after after motion has begun, the tangential acceleration is:

A stationary particle explodes into two particles of masses $m_1$ and $m_2$ which more in opposite direction with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1 / E_2$ is: