Center of Mass and Collision

Two particles of masses $2$ g and $4$ g are situated at the opposite ends, A and B of a wooden bar respectively. Let $l(AB) = 9$ cm. The center of mass of the system will be

Three identical spheres, each of mass 'm' kg, are kept as shown in the figure, touching each other, with their centers on a straight line. If their centers are marked as A, B, C respectively, the distance of center of mass of the system fro...

Two masses $m_1$ and $m_2$ moving with velocities $V_1$ and $V_2$ in opposite directions collide elastically and after collision $m_1$ and $m_2$ move with velocities $V_2$ and $V_1$ respectively. The ratio $\dfrac{m_2}{m_1}$ is

In case of perfectly elastic collision,

A stationary body explodes into two parts of masses $M_1$ and $M_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of their kinetic energies is

A mass M moving with velocity V along X-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3V. The velocity of the combination, after the collision is

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

A sphere of mass ' $m$ ', moving with velocity ' $3 u$ ' collides head-on with another identical sphere at rest. If ' $e$ ' is coefficient of restitution then what will be the ratio of velocity of the second sphere to that of first sphere a...

An object of mass ' $m$ ' moving with velocity ' $u$ ' collides with another stationary object of mass ' $M$ ' and stops just after the collision. The coefficient of restitution is

There is head-on elastic collision between the two particles moving in the same direction with speeds $5 \mathrm{~m} / \mathrm{s}$ and $3 \mathrm{~m} / \mathrm{s}$ respectively. After collision, the velocity of the first particle becomes $4...

In the system of two particles of masses ' $\mathrm{m}_1$ ' and ' $\mathrm{m}_2$ ', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by...

A metal rod of weight ' $W$ ' is supported by two parallel knife-edges A and B . The rod is in equilibrium in horizontal position. The distance ' between two knife-edges is ' $r$ '. The centre of mass of the rod is at a distance ' $x$ ' fro...

In projectile motion two particles of masses $\mathrm{m}_1$ and $m_2$ have velocities $\vec{V}_1$, and $\vec{V}_2$ respectively at time $t=0$. Their velocities become $\overline{V_1^{\prime}}$ and $\overrightarrow{V_2^{\prime}}$ at time 2 t...

A meter scale is supported on a wedge at its centre of gravity. A body of weight ' $w$ ' is suspended from the 20 cm mark and another weight of 25 gram is suspended from 74 cm mark balances it and the meter scale remains perfectly horizonta...

In case of system of two-particles of different masses, the centre of mass lies

Three identical metal balls each of radius ' $r$ ' are placed such that an equilateral triangle is formed when centres of three ball are joined. The centre of mass of the system is located at

A particle of mass m collides with another stationary particle of mass $M$. The particle $m$ stops just after collision. The coefficient of restitution is

1000 small balls, each weighing 1 gram, strike one square cm of area per second with a velocity $50 \mathrm{~m} / \mathrm{s}$ in a normal direction and rebound with the same velocity. The value of pressure on the surface will be

A moving body with mass ' $\mathrm{m}_1$ ' strikes a stationary mass ' $\mathrm{m}_2$ '. What should be the ratio $\frac{m_1}{m_2}$ so as to decrease the velocity of first by (1.5) times the velocity after the collision?

A body falls on a surface of coefficient of restitution 0.6 from a height of \(1 \mathrm{~m}\). Then the body rebounds to a height of

Consider the following statements \(\mathrm{A}\) and \(\mathrm{B}\). Identify the correct choice in the given answers.
A. In an inelastic collision, there is no loss in kinetic energy during collision.
B. During a collision, the linear mome...

A person with machine gun can fire 50 g bullets with a velocity of \(240 \mathrm{~m} / \mathrm{s}\). A \(60 \mathrm{~kg}\) tiger moves towards him with a velocity of \(12 \mathrm{~m} / \mathrm{s}\). In order to stop the tiger in track, the ...

A simple spring has length \(l\) and force constant \(K\). It is cut in to two springs of length \(l_1\) and \(l_2\) such that \(l_1=n l_2\)(\(n\) is an integer). The force constant of spring of length \(l_1\) is

A particle of mass '\(m\)' moving east ward with a speed '\(v\)' collides with another particle of same mass moving north-ward with same speed '\(v\)'. The two particles coalesce after collision. The new particle of mass '\(2 \mathrm{~m}\)'...

A ball kept at \(20 \mathrm{~m}\) height falls freely in vertically downward direction and hits the ground. The coefficient of restitution is 0.4. Velocity of the ball first rebound is \(\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]\)

A mass '\(\mathrm{M}\)' moving with velocity '\(\mathrm{V}\)' along \(\mathrm{X}\)-axis collides and sticks to another mass \(2 \mathrm{M}\) which is moving along \(\mathrm{Y}\)-axis with velocity '\(3 \mathrm{~V}\)'. The velocity of the co...

Two massless springs of spring constant \(\mathrm{K}_1\) and \(\mathrm{K}_2\) are connected one after the other forming a single chain, suspended vertically and certain mass is attached to the free end. If '\(e_1\)' and '\(e_2\)' are their ...

A wooden black of mass '\(\mathrm{m}\)' moves with velocity '\(\mathrm{V}\)' and collides with another block of mass '\(4 \mathrm{~m}\)', which is at rest. After collision the block of mass '\(\mathrm{m}\)' comes to rest. The coefficient of...

Force is applied to a body of mass \(2 \mathrm{~kg}\) at rest on a frictionless horizontal surface as shown in the force against time \((F-t)\) graph. The speed of the body after 1 second is

A particle of mass '\(m\)' collides with another stationary particle of mass '\(M\)'. A particle of mass '\(\mathrm{m}\)' stops just after collision. The coefficient of restitution is

A molecule of mass 'm' moving with velocity 'v' makes 5 elastic collisions with a wall of container per second. The change in momentum of the wall per second in 5 collisions will be

Two masses '\(m_{\mathrm{a}}\)' and '\(\mathrm{m}_{\mathrm{b}}\)' moving with velocities '\(v_{\mathrm{a}}\)' and '\(v_{\mathrm{b}}\)' opposite directions collide elastically. Alter the collision '\(m_a\)' and '\(m_b\)' move with velocities...

$N$ number of balls of mass $m \mathrm{~kg}$ moving along positive direction of $X$ - axis, strike a wall per second and return elastically. The velocity of each ball is $u \mathrm{~m} / \mathrm{s}$. The force exerted on the wall by the bal...

In system of two particles of masses $m_1$ and $m_2$, the first particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance

A bullet of mass \(m\) moving with velocity \(v\) is fired into a wooden block of mass \(M\), If the bullet remains embedded in the block, the final velocity of the system is

A batsman hits a ball of mass 0.2 kg straight towards the bowler without changing its initial speed of \(6 \mathrm{~m} / \mathrm{s}\). What is the impulse imparted to the ball?

A block of mass ' $m$ ' moving on a frictionless surface at speed ' $v$ ' collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle ' $\theta$ ' with its initial direction and has speed ' $v_1$...