Block A is placed on cart B as shown in figure . If the coefficient of static and kinetic friction between the 20 kg block A and 100 kg cart B are both essentially the same value of `0.5` : (g = `10 m//s^(2)`)

Options

A. the blocks A and B will have a common acceleration if P = 60 N
B. acceleration of cart B is `0.98 m//s^(2)` if P = 40 N
C. acceleration of cart B is greater than that of A is P = 60 N
D. the common acceleration of both the blocks is `0.667 m// s^(2) ` if P = 40 N

Answer

A, D

Explanation

`2P - f_(1)= 20 xx a " " ……(i) `
As `" " 2P = (120) xx a " " …..(ii) `
`a = (P)/(60)`
`2P - (5)/(10)xx 200 = 20 xx (P)/(60)`
`2P - (P)/(3) = 100`
`(5P)/(3) = 100`
`P = 60 N`