Find the acceleration of the body if a force `F = 8 N` pulls the string at `P` that passes over the body and it is connected by another string to a rigid support at `Q`. (Take radius of gyration `k = (2)/(sqrt(3)) m, R = 2 m, r = 1 m`, and mass of the body `m = 3 kg`).
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Options

A. `1 m//s^2`
B. `1.5 m//s^2`
C. `1.2 m//s^2`
D. `2 m//s^2`

Answer

A

Explanation

(a) `a = prop R`
`F - T = ma`…(i)
Torque about `C` :
`TR - Fr = I prop`
`rArr TR - Fr = mk^2 (a)/(R )`
Put the value of `T` from equation (i)
`(F - ma) R - Fr = (mk^2 a)/( R)`
`F(R - r) = a[(mk^2)/(R) + mR]rArr a = (FR (R - r))/((k^2 + R^2)m)`
=`(8 xx 2 xx (2 - 1))/((4/(3) + 4) xx 3) = (8 xx 2 xx 1)/(4 xx 4/3 xx 3) = 1 m//s^2`.
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