Question

In the figure shown. Find accelerations of 1 kg, 2 kg and 3 kg blocks $(g=10m/s^2)$

• A. acceleration of 1 Kg block is $\frac{20}{11}$
• B. acceleration of 2 Kg block is $\frac{50}{11}$
• C. acceleration of 1 Kg block is $\frac{50}{11}$
• D. acceleration of 3 Kg block is $\frac{70}{11}$

Answer 1

Answer: (B), (D)

acceleration of 2 Kg block is $\frac{50}{11}$
acceleration of 3 Kg block is $\frac{70}{11}$

From the pulley $P_2$ we see that
$2T_1=2T_2\therefore T_1=T_2$ .....(i)
Let the acceleration of 1 kg block be $a$ and that of 2 kg and 3 kg block be $a_r$

The acceleration of both the pulleys is thus $a/2$
1 kg $T_2=\left(1\right)\left(a\right)$ .....(ii)
2 kg $T_1-20=2(a_r-\frac{a}{2})$ .....(iii)
3 kg $30-T_1=3(a_r+\frac{a}{2})$ .....(iv)

On solving these equations, we get
$T_1=T_2=\frac{120}{11}N$
$a_1=a=\frac{120}{11}m/s^2$
$a_2=a_r-\frac{a}{2}=-\frac{50}{11}m/s^2$
or $a_2=\frac{50}{11}m/s^2$ (downwards)
$a_3+a_r+\frac{a}{2}=\frac{70}{11}m/s^2$ (downwards).