Question

A block of mass 12 kg is hanging with a light string in a lift as shown in figure (a). The lift is moving in the upward direction and its speed time graph is plotted as shown in figure (b) : (take $g=10m/s^2$)

Which of the following is possible?

• A. Tension in the rope at $t=2sec$ is $120N$
• B. Tension in the rope at $t=8sec$ is $120N$
• C. Tension in the rope at $t=11sec$ is$168N$
• D. Tension in the rope at $t=2sec$ is $144N$

Answer 1

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

Tension in the rope at $t=11sec$ is$168N$
Tension in the rope at $t=2sec$ is $144N$
Tension in the rope at $t=8sec$ is $120N$

In the time interval $t=0$ to $t=5$, the acceleration $a=\frac{10-0}{5-0}=2m/s^2$
Hence, $T=m(g+a)$
$T=12\times (10+2)=144N$
In the time interval $t=5$ to $t=10$, the acceleration $a=0$
Hence, $T=mg=12\times 10=120N$
In the time interval $t=10$ to $t=15$, the acceleration $a=\frac{30-10}{15-10}=4m/s^2$
Hence, $T=m(g+a)$
$T=12\times (10+4)=168N$