A block of mass M with a semicircualr of radius R, rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest the top point A The cylinder slips on the semicircular frictionless track. How far has the block moved when the cylinder reaches the bottom (point B) of the track ? How fast is the block moving when the cylinder reaches the bottom of the track?

Answer

B

Explanation

(i)
`Mx=m(R-r-x)`
`:. x=(m(R-r))/(M+m)`
(ii)
`:. sqrt(2K_MM)=sqrt(2K_mm)`
`:. (K_M)/(K_m)=m/M` …(i)
`K_m+K_m=` decrease in potential energy of `m`
`=mg(R-r)` ...(ii)
Solving these two equations we get,
`K_M=((m)/(M+m))mg(R-r)=1/2Mv_M^2`
`:. v_M=msqrt((2g(R-r))/(M(M+m)))`