Coefficient of friction between pulley and light string is `mu_(1)`. Calculate minimum coefficient of friction between block `A` and ground such that system can be in equibrium.

Options

A. `mu=2`
B. `mu=2e^((-mupi)/(2))`
C. `mu=e^((mu_(1)pi)/(2))`
D. `mu=(3)/(2)`

Answer

B

Explanation

`dT=mu_(1)Td theta underset((mum_(0)g)/(2))overset(m_(o))int(dT)/(T)=mu_(1)underset((0)/(2))overset((pi)/(2))intd theta=mu_(1)(pi)/(2)`
`[ln T]_((mum_(0)g)/(2))^(m_(0)g)=(mu_(1)pi)/(2)` ln`(2)/(mu)=(mu_(1)pi)/(2)`
`(mu)/(2)=e^((mu_(1)pi)/(2)) mu=2e"^(mu_(1)pi)/2`