In the arrangment shown in figure, `m_(A)`=1 kg, `m_(B)`=4 kg. String is light and inextensible while pulley is smooth. Coefficient of friction between block A and the table is `mu`=0.2. Find the speed of both the blocks when block B has descended a height h=1 m. (Take ,g=10 `ms^(-2)`)

Explanation

From constraint relation, we see that
`v_(A)=v_(B)=v`
Force of friction between block A and table will be
`f=mum_(A)g=(0.2)(1)(10)=2N`
`:. W_(nc)=DeltaU+DeltaK`
`:. -fs=-m_(B)gh+(1//2)(m_(A)+m_(B))v^(2)`
or `" " (-2)(1)=-(4)(10)(1)+(1)/(2)(4+1)v^(2)`
`-2=-40+2.5 v^(2) " or " 2.5 v^(2)=38`
`:. v^(2)=15.2 m^(2) s^(-2) " or " v=3.9 ms^(-1)`