A block of mass `m` slides 0n a frictionless table. It is constrained to move inside a ring of radius `R` . At time `t=0` , block is moving along the inside of the ring (i.e. in the tangential direction) with velocity `v_(0)` . The coefficient of friction between the block and the ring is `mu` . Find the speed of the block at time `t` .

Answer

A

Explanation

`N=(mv^(2))/(R)`
`f_(max)=muN=(mumv^(2))/(R)`
:. Retardation `a=(f_(max))/(m)`
`=(muv^(2))/(R)`
:. `(-(dv)/(dt))=(muv^(2))/(R)`
or `int_(v_(0))^(v)(dv)/(v^(2))=-(mu)/(R)int_(0)^(t)dt`
or `v=(v_(0))/(1+(muv_(0)t)/(R))`