Question

From the given figure where all pulleys are ideal and $g=10m/s^2$

• A. acceleration of 2 kg is downwards
• B. acceleration of 4 kg is $\frac{10}{11}m/s^2$
• C. tension T given in figure is $\frac{60}{11}N$
• D. acceleration of 2 kg is $\frac{80}{11}m/s^2$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A acceleration of 2 kg is downwards
B acceleration of 4 kg is $\frac{10}{11}m/s^2$
C tension T given in figure is $\frac{60}{11}N$
D acceleration of 2 kg is $\frac{80}{11}m/s^2$

By constraint relation $\Rightarrow 8T{a}_4=T{a}_2\Rightarrow a_2=8a_4$

Let $a_4=a$ upwards. So $a_2=8a$ downwards.

Applying F = ma for 2 kg block,
$20-T=2\times 8a\Rightarrow 20-T=16a\dots \left(1\right)$
Applying F = ma for 8 kg block,
$8T-40=4a\dots \left(2\right)$
From (1) and (2),

$a=\frac{10}{11}m/s^2=a_4$

$a_2=8\times a=8\times \frac{10}{11}=\frac{80}{11}m/s^2$

$T=6\times a=6\times \frac{10}{11}=\frac{60}{11}N$