A rod AB moves with a uniform velocity v in a uniform magnetic field as shown in figure
(##HCV_VOL2_C38_E01_033_Q01##)

Options

A. Both planks have same acceleration
B. Net force sphere is non-zero
C. `F_(1)+F_(2)=(17)/(5)ma`
D. `f=5ma`

Answer

C

Explanation

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`