Question

The acceleration of block A at the given instant is

Answer 1

Answer:

$(3) \frac{g}{17}$

Explanation:

1)

Let the acceleration of Block A be $a_1$ and that of Block B be $a_2.$

Since, right string on block A pulley is at rest and left one has acceleration

as $a_2cos(60^{\circ})$

By Pulley constraint ,

$a_1=\frac{a_2cos(60^{\circ})+0}{2}=\frac{a_2}{4}$

2)

Applying Newton's Law on Block A,

$mg-2T=ma_1$

Again on Block B,

$Tcos(60^{\circ})=ma_2\\ \\=>T=2ma_2=8ma_1$

3) Using above two equations,

$mg-2*8ma_1=ma_1\\ \\=>a_1=\frac{g}{17}$

Hence, Acceleration of block A is $\boxed{\frac{g}{17}}$

Answer 2

Let the acceleration of Block A be a1 and that of Block B be a2

Since, right string on block A pulley is at rest and left one has acceleration

as a2cos60deg

By Pulley constraint ,

a1=a2/4

mg-2T=ma1

Tcos60deg=ma2

T=2ma2=8ma1

mg-16ma1=ma1

a1=g/17