Question

When a train starting from rest is uniformly accelerating, a plumb bob hanging from the roof of a compartment is found to be inclined at an angle of ${45}^0$ with the vertical. The time taken by the train to travel a distance of 1/2 km will be nearly

• A. 7 s
• B. 10 s
• C. 15 s
• D. 25 s

Answer 1

Answer: (B)

10 s

Taking, $g=10m/s^2$,
Since the bob makes a ${45}^0$ angle with vertical, total force (including pseudo force), and hence in vertical direction equals that of horizontal direction.
$mg=ma$

$a=g=10m/s^2$

$s=\frac{1}{2}a{t}^2=\frac{1}{2}km$

$10m/s^2\times t^2=1000m$

$t^2=100$

$t=10s$