Two blocks `(m and M)` are arranged as in figure Then is friction between ground and `M` only and other surface are frictionless between ground and `M is mu = 0.25` The maximum ratio of `m` and `M(m//M)` so that the system remain is at rest

Options

A. `(1)/(3)`
B. `(1)/(4)`
C. `3`
D. none of these

Answer

a

Explanation

AS sphere is at rest
`T = mg` …(i)
`f = T`…(ii)
and `f le muN`
Here `N = Mg + T = (M+ m)g`
`T le mu (M +m)g`
`mg le mu(M + m)g`
`(m)/(M) le (mu)/((1 - mu))`
`(m)/(M) le (0.25)((1 - 0.25)) rArr (m)/(M) le (1)/(3)`