A trolley of mass 20 kg is attached to a block of mass 4kg by massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between trolley and the surface is 0.02, then the acceleration of the trolley and block system is `(Take g=10ms^(-2))`

Options

A. `1"ms"^(-2)`
B. `2"ms"^(-2)`
C. `1.5"ms"^(-2)`
D. `2.5"ms"^(-2)`

Answer

C

Explanation

As the string in inextensible, and pulley is smooth, therefore both 4kg block and the 20 kg trolly have the same acceleration a.
Let T be tension in the string. The equation of motion of the block is 40-T=4a
The equation of motion of the trolley is `T-f_(k)=20a`
`f_(k)=mu_(k)N`
`Here, mu_(k)=0.02, N=20xx10=200N `
`therefore T-0.02xx200=20a or T-4=20a....(ii)`
Adding (i) and (ii), we get `a=(36)/(24)ms^(-2)=1.5ms^(-2)`