A man of mass m_1 is standing at a height h f | vedclass

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

Question

(C) In a gravity-free room,the center of mass of the system remains at rest because there are no external forces acting on the system.Let the man move

Vedclass · Accepted Answer

$\left( 1 + \frac{m_2}{m_1} \right) h$

Vedclass · Answer

(C) In a gravity-free room,the center of mass of the system remains at rest because there are no external forces acting on the system.Let the man move upwards with velocity $v$ when he throws the ball downwards with velocity $u$.By the law of conservation of linear momentum,the initial momentum is zero:$m_1 v - m_2 u = 0 \implies v = \frac{m_2 u}{m_1}$.The time taken by the ball to reach the floor is $t = \frac{h}{u}$.During this time,the man moves upwards by a distance $d = v 	imes t = \left( \frac{m_2 u}{m_1} ight) 	imes \left( \frac{h}{u} ight) = \frac{m_2}{m_1} h$.The initial height of the man was $h$. Since he moves upwards by $\frac{m_2}{m_1} h$,his new distance from the floor is $h + \frac{m_2}{m_1} h = \left( 1 + \frac{m_2}{m_1} ight) h$.

$A$ man of mass $m_1$ is standing at a height $h$ from the floor in a gravity-free room. He throws a ball of mass $m_2$ downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the floor.

Similar Questions

$A$ bullet of mass $m$ is fired from a gun of mass $M$. If the velocity of the bullet is $v$,what will be the recoil velocity of the gun?

$A$ 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:

$A$ bomb of mass $9\,kg$ explodes into $2$ pieces of mass $3\,kg$ and $6\,kg.$ The velocity of the $3\,kg$ mass is $1.6\,m/s.$ The kinetic energy of the $6\,kg$ mass is ............ $J.$

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is : (in $ms^{-1}$ )

Vedclass Test Series

Exam Paper Generator

Online Exam Module