As shown in figure, `A` and `B` are two blocks of mass `5 kg` and `10 kg` connected by inextensible and massless strings. Pulleys `1,2,3` are massless, no frction exists between pully and strings. The coefficient of friction between blocks `B` and the surface is `mu=0.1` Take `g=10m//s^(2)`. Choose the correct statements.

Options

A. The acceleration of block `A` is `0.06ms^(-2)`
B. The acceleration of block `B` is `0.24 ms^(-2)`
C. The tension in the string connecting pulley `1` and block `A` is `24.7N`
D. The tension in the string connecting pulley `3` and block `B` is `6.175 N`

Answer

A, B

Explanation

`y_(1)+(y_(1)-y_(0))+x=1_(1)`….(1)

`y_(2)+(y_(2)-y_(1))=1_(2)`....(2) `v_(B)=4v_(A)`
`a_(B)=4a_(A) m_(A)g-T=m_(a)a_(A)`
`(T)/(4)-muM_(B)g=M_(B)a_(B) , M_(A)g-T=M_(a)a_(A)`
`T-4muM_(B)g=M_(B)4a_(B)=M_(B)16 a_(a)`
(1) `a_(A)=[(M_(A)-4muM_(B))/(16M_(B)+M_(A))]=(5-4xx0.1xx10)/((16xx10)+5)x10`
`-(10)/(165)=0.06ms^(-2)`
(2) `a_(B)=4a_(A)=0.2ms^(-2)`
(3) `T=m_(A)(g-a_(A))`
(Between `A` and pulley `1`)`= 5[10-0.06]=50N`
(4) `(T)/(4)=12.5N` ( Between pulley `3` and block`B`)