JEE Main Center of Mass and Collision Practice Questions With Solutions

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be :

(g = 10 m/s²)

The figure represents the momentum time ($\mathrm{p}-\mathrm{t}$p - t) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively?

If $(t_3-t_2)<t_1$\left(\right. t_{3} - t_{2} \left.\right) < t_{1}

A ball of mass $200\mathrm{g}$200 \textrm{ } g rests on a vertical post of height $20\mathrm{m}$20 \textrm{ } m. A bullet of mass $10\mathrm{g}$10 \textrm{ } g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\mathrm{m}$30 \textrm{ } m and the bullet at a distance of $120\mathrm{m}$120 \textrm{ } m from the foot of the post. The value of initial velocity of the bullet will be (if $g=10\mathrm{m}/{\mathrm{s}}^2$g = 10 \textrm{ } m / s^{2}) :

If momentum of a body is increased by 20%, then its kinetic energy increases by

Two bodies of mass $1\mathrm{kg}$1 \textrm{ } kg and $3\mathrm{kg}$3 \textrm{ } kg have position vectors $\hat{i}+2\hat{j}+\hat{k}$\hat{i} + 2 \hat{j} + \hat{k} and $-3\hat{i}-2\hat{j}+\hat{k}$- 3 \hat{i} - 2 \hat{j} + \hat{k} respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

In two different experiments, an object of mass $5\mathrm{kg}$5 \textrm{ } kg moving with a speed of $25{\mathrm{ms}}^{-1}$25 \left(\textrm{ } ms\right)^{- 1} hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

A body of mass $10\mathrm{kg}$10 \textrm{ } kg is projected at an angle of ${45}^{\circ }$45^{\circ} with the horizontal. The trajectory of the body is observed to pass through a point $(20,10)$\left(\right. 20 , 10 \left.\right). If $\mathrm{T}$T is the time of flight, then its momentum vector, at time $\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$t = \frac{T}{\sqrt{2}}, is _____________.

[Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$g = 10 \textrm{ } m / s^{2} ]

A ball of mass $0.15\mathrm{kg}$0.15 \textrm{ } kg hits the wall with its initial speed of $12{\mathrm{ms}}^{-1}$12 \left(\textrm{ } ms\right)^{- 1} and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $100\mathrm{N}$100 \textrm{ } N, calculate the time duration of the contact of ball with the wall.

A body of mass $8\mathrm{kg}$8 \textrm{ } kg and another of mass $2\mathrm{kg}$2 \textrm{ } kg are moving with equal kinetic energy. The ratio of their respective momentum will be :

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms^$-$-1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?