Shown in the diagram is a system of two bodies, a block of mass m and a disc of mass 4m, held in equilibrium. If the string 3 is burnt, find the acceleration of the disc. Neglect the masses of the pul

Question

Shown in the diagram is a system of two bodies, a block of mass m and a disc of mass 4m, held in equilibrium. If the string 3 is burnt, find the acceleration of the disc. Neglect the masses of the pulleys P and Q . The co-efficient of friction between the block and horizontal surface is 0.5 and friction between disc and string is zero.

TestHub · Accepted Answer

After string 3 is burnt, let tension in the string connecting block and pulley P be T , so tension in various segments is shown below.

From virtual work method :

$Ta_{2} - 4 Ta_{1} = 0$

$\Rightarrow a_{2} = 4 a_{1} .. \dots\dots (i)$

Let

a_{1}

be a , then

a_{2} = 4 a

Now from FBD of disc :

$4 mg - 4 T = 4 ma .. \dots\dots\dots (ii)$

Now from FBD of block :

$T - μ mg = m (4 a)$ .......(iii)

on addin (ii) & (iii)

$mg [1 - μ] = 5 ma$

$\Rightarrow a = \frac{g}{5} \times \frac{1}{2}$

$a = \frac{g}{10}$

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