Mechanics PYQ — Page 21

Consider a system of two particle having masses $m_1$ and $m_2$. If the particle of mas $m_1$ is pushed towards the mass centre of particle through a distance $d$, by what distance would the particle of mass $m_2$ move so as to keep the mass centre of particles at the original position?

A wheel having moment of inertia $2 \mathrm{~kg}$ $\mathrm{m}^2$ about its vertical axis, rotates at the rate of $60 \mathrm{rpm}$ about the axis. The torque which can stop the wheel's rotation in one minute would be:

The dimensions of universal gravitational constant are:

A stone is tied to a string of length ' $l$ ' and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed ' $u$ '. The magnitude of change in velocity as it reaches a position where the string is horizontal ( $g$ being acceleration due to gravity)is:

If $|\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $|\vec{A} + \vec{B}|$ is:

An round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $\mathrm{I}_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:

The unit of permittivity of free space $\varepsilon_0$, is:

The density of a newly discovered plant is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth $R$, the radius of the planet would be:

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 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:

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? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

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 $\mathrm{B}$ ?

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

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?

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:

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:

A disc is rotating with angular speed $\omega$. If a child sits on it, what is conserved?

A block of mass $10 \mathrm{~kg}$ placed on the rough horizontal surface having coefficient of friction $\mu=0.5$, if a horizontal force of $100 \mathrm{~N}$ acting on it then acceleration of the block will be:

A circular disc is to be made by using iron and aluminium so that it acquire moment of inertia about the geometrical axis. It is possible with: