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A uniform sphere of mass m is positioned...

A uniform sphere of mass m is positioned between two horizontal planks `A` and `B` of mass `2m` and `m` respectively as shown. Ground surface is smooth and friction between planks and sphere is sufficient so that no slipping takes place. Horizontal forces `F_(1)` and `F_(2)` are applied on plank so that acceleration of sphere is zero. Plank `B` is moving toward right with acceleration a. Which of the following is/are correct ?

A

Both planks have same acceleration

B

Net force sphere is non-zero

C

`F_(1)+F_(2)=(17)/(5)ma`

D

`f=5ma`

Text Solution

Verified by Experts

The correct Answer is:
C
A uniform ……………..
Since sphere is at rest both friction at top and bottom will be equal as acceleration of sphere is zero. Acceleration of both planks

`a_(1)=a_(2)=alpha R=a` `:.` No slipping
`F_(1)-f=ma` ......(1)
`F_(2)-f=2ma` .......(2)
`2fR = (2)/(5)mR^(2)alpha`
`implies 2fR = (2)/(5)ma`
adding equation (1), (2) and (3)
`E_(1)+F_(2) = (3+(2)/(5))ma = (17)/(5)ma`
`x = 7`
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