A sphere P of mass m moving with velocity v u | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a perfectly elastic collision between two identical masses where one is initially at rest,the conservation of linear momentum and kinetic ener

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) For a perfectly elastic collision between two identical masses where one is initially at rest,the conservation of linear momentum and kinetic energy leads to the following equations:$1$. Conservation of linear momentum: $m\vec{v} = m\vec{v}_P + m\vec{v}_Q$,which simplifies to $\vec{v} = \vec{v}_P + \vec{v}_Q$.$2$. Conservation of kinetic energy: $\frac{1}{2}mv^2 = \frac{1}{2}mv_P^2 + \frac{1}{2}mv_Q^2$,which simplifies to $v^2 = v_P^2 + v_Q^2$.From the momentum equation,we can write $v^2 = |\vec{v}_P + \vec{v}_Q|^2 = v_P^2 + v_Q^2 + 2v_P v_Q \cos 	heta$.Comparing this with the kinetic energy equation $v^2 = v_P^2 + v_Q^2$,we get $2v_P v_Q \cos 	heta = 0$.Since $v_P$ and $v_Q$ are non-zero,we must have $\cos 	heta = 0$,which implies $	heta = 90^o$.

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.

Similar Questions

$A$ sphere of mass $10 \ kg$ moving with a velocity of $10 \ m/s$ undergoes an elastic collision with a body of mass $5 \ kg$ moving in the same direction with a velocity of $4 \ m/s$. What are their velocities after the collision?

$A$ particle of mass $m$,moving with a velocity $v$,makes an elastic collision in one dimension with a stationary particle of mass $m$. During the collision,they remain in contact with each other for an extremely small time $T$. Their force of contact with time is shown in the figure. Then $F_0 =$

Which of the following statements is true?

$A$ billiard ball moving with a speed of $5 \, m/s$ collides with an identical ball originally at rest. If the first ball stops after collision,then the second ball will move forward with a speed of ........... $m/s$.

$A$ body falling on the ground from a height of $10 \, m$,rebounds to a height of $2.5 \, m$. The ratio of the velocities of the body just before and after the collision will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module