A cat with mass m_c is sitting at rest on the | vedclass

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

Question

(B) Let the left plank be $P_1$ and the right plank be $P_2$. Initially,the system is at rest. When the cat leaps from $P_1$ to $P_2$ with speed $v_{c

Vedclass · Accepted Answer

$\frac{2m_c v_{cg}}{m_s}$

Vedclass · Answer

(B) Let the left plank be $P_1$ and the right plank be $P_2$. Initially,the system is at rest. When the cat leaps from $P_1$ to $P_2$ with speed $v_{cg}$ (to the right),by conservation of momentum for the system (cat + $P_1$): $0 = m_c v_{cg} + m_s v_{P1} \implies v_{P1} = -\frac{m_c v_{cg}}{m_s}$ (to the left). When the cat lands on $P_2$,the cat and $P_2$ move together. By conservation of momentum for the system (cat + $P_2$): $m_c v_{cg} = (m_c + m_s) v_{P2} \implies v_{P2} = \frac{m_c v_{cg}}{m_c + m_s}$. When the cat leaps back from $P_2$ to $P_1$ with speed $v_{cg}$ (to the left),let the final velocity of $P_2$ be $v'_{P2}$. By conservation of momentum for the system (cat + $P_2$): $(m_c + m_s) v_{P2} = m_c (-v_{cg}) + m_s v'_{P2}$. Substituting $v_{P2}$: $(m_c + m_s) \left( \frac{m_c v_{cg}}{m_c + m_s} \right) = -m_c v_{cg} + m_s v'_{P2}$. $m_c v_{cg} = -m_c v_{cg} + m_s v'_{P2} \implies 2m_c v_{cg} = m_s v'_{P2} \implies v'_{P2} = \frac{2m_c v_{cg}}{m_s}$.

Similar Questions

$A$ shell,in flight,explodes into four unequal parts. Which of the following is conserved?

$A$ particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is

$A$ 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:

$A$ man of mass $m$ is standing on a platform of mass $M$ kept on a smooth ice surface. If the man starts moving on the platform with a speed $v$ relative to the platform,with what velocity does the platform recoil relative to the ice?

Vedclass Test Series

Exam Paper Generator

Online Exam Module