A ball of mass m suspended from a rigid suppo | vedclass

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

Question

(D) Let the velocity of the ball of mass $m$ just before the collision be $u$. By conservation of energy, $\frac{1}{2}mu^2 = mgh$, so $u = \sqrt{2gh}$

Vedclass · Accepted Answer

$\frac{h}{9}$

Vedclass · Answer

(D) Let the velocity of the ball of mass $m$ just before the collision be $u$. By conservation of energy, $\frac{1}{2}mu^2 = mgh$, so $u = \sqrt{2gh}$.In an elastic collision, both kinetic energy and linear momentum are conserved.Let $v_1$ be the velocity of the ball (in the opposite direction) and $v_2$ be the velocity of the block after the collision.Conservation of momentum: $mu = 2mv_2 - mv_1 \Rightarrow u = 2v_2 - v_1 \quad \dots (i)$Conservation of kinetic energy: $\frac{1}{2}mu^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}(2m)v_2^2 \Rightarrow u^2 = v_1^2 + 2v_2^2 \quad \dots (ii)$From $(i)$, $2v_2 = u + v_1$. Substituting this into $(ii)$:$u^2 = v_1^2 + 2\left(\frac{u+v_1}{2}\right)^2 = v_1^2 + \frac{(u+v_1)^2}{2}$$2u^2 = 2v_1^2 + u^2 + v_1^2 + 2uv_1$$u^2 - 2uv_1 - 3v_1^2 = 0$$(u - 3v_1)(u + v_1) = 0$Since $v_1$ is the speed in the opposite direction, $v_1 = \frac{u}{3}$.The new height $h'$ reached by the ball is given by $mgh' = \frac{1}{2}mv_1^2$.$h' = \frac{v_1^2}{2g} = \frac{(u/3)^2}{2g} = \frac{u^2}{18g} = \frac{2gh}{18g} = \frac{h}{9}$.

Similar Questions

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $5$ times its mass (in $\%$)? (Assume the collision to be head-on elastic collision)

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is:

$A$ sphere of mass $0.1\,kg$ is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension,this sphere hits a block of the same mass at rest on a frictionless table. If the impact is elastic,then the kinetic energy of the block after the collision is ............. $J$.

$A$ body of mass $M_1$ collides elastically with another mass $M_2$ at rest. There is maximum transfer of energy when

An object of mass $M_1$ moving horizontally with speed $u$ collides elastically with another object of mass $M_2$ at rest. Select the correct statement.

Vedclass Test Series

Exam Paper Generator

Online Exam Module