Question

In the given figure, pulley is massless and a force $F=10t$ is applied on it. Here, $t$ is time. $[g=10m/s^2]$

• A. Time when $4$ kg leaves the ground is $8$ sec.
• B. At t = 3 sec, speed of 2 kg is 4 m/s.
• C. Power of tension force on 2 kg when 4 kg leaves ground is 800 Watt.
• D. Speed of 2 kg when 4 kg leaves ground is 20 m/s.

Answer 1

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

The correct options are
A Time when $4$ kg leaves the ground is $8$ sec.
C Power of tension force on 2 kg when 4 kg leaves ground is 800 Watt.
D Speed of 2 kg when 4 kg leaves ground is 20 m/s.

$\Rightarrow F=2T\Rightarrow 10t=2T\Rightarrow T=5t$
To lift 4 kg, $T=mg=40N$
$\Rightarrow 5t=40,t=8sec$
To lift 2 kg,
T = 20 N
$\therefore t=4sec$
FBD of 2 kg block,

For $t>4sec\Rightarrow 5t-20=2a$
$a=\frac{5}{2}t-10\Rightarrow {\int }_0^{v}dv={\int }_4^8(\frac{5}{2}t-10)dt$
$v=(\frac{5}{4}{t}^2-10t{)}_4^8\Rightarrow v=20m/s$
Therefore, power = $F\times v$ = $=F\times v=5t\times v=5\times 8\times 20=800W$