A block of mass M with the semicircular track of radius R rests on a horizontal smooth surface. A cylinder of radius r slips on the track. If the cylinder is released from rest from the top, the distance moved by block when the cylinder reaches the bottom of the track is

Question

A block of mass M with the semicircular track of radius R rests on a horizontal smooth surface. A cylinder of radius r slips on the track. If the cylinder is released from rest from the top, the distance moved by block when the cylinder reaches the bottom of the track is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-tpftxrc0k2yq.png" /> (A) R-r (B) (m (R - r)/M + m) (C) (M/M + m) (R - r) (D) (M/M - m) r

Tardigrade Admin · Accepted Answer

COM of system (B l o c k + c y l i n d e r) remains at rest. If x is the distance moved by block when cylinder moves from top to bottom (M + m) x=m (R - r) X=(m (R - r)/M + m)

Q. A block of mass $M$ with the semicircular track of radius $R$ rests on a horizontal smooth surface. A cylinder of radius $r$ slips on the track. If the cylinder is released from rest from the top, the distance moved by block when the cylinder reaches the bottom of the track is

$R - r$

$\frac{m ( R - r )}{M + m}$

$\frac{M}{M + m} (R - r)$

$\frac{M}{M - m} r$

COM of system $(Bl oc k + cy l in d er)$ remains at rest. If $x$ is the distance moved by block when cylinder moves from top to bottom $(M + m) x = m (R - r)$
$X = \frac{m ( R - r )}{M + m}$

Q. A block of mass M with the semicircular track of radius R rests on a horizontal smooth surface. A cylinder of radius r slips on the track. If the cylinder is released from rest from the top, the distance moved by block when the cylinder reaches the bottom of the track is

R−r

M+mm(R−r)​

M+mM​(R−r)

M−mM​r