Question

56. A bob is hanging over a pulley inside a car through
a string. The second end of the string is in the hand
of a person standing in the car. The car is moving
with constant acceleration ‘a' directed horizontally
as shown in figure . Other end of the string is pulled
with constant acceleration ‘a (relative to car)
vertically. The tension in the string is equal to
car​

Answer 1

car is moving forward direction with an acceleration a. so, bob are in non-inertial frame of reference. to make inertial frame of reference apply same acceleration on bob just opposite direction (i.e., west )

so, acceleration acting on bob , a' = -a i - g j

so, magnitude of acceleration, a' = √(a² + g²) along string. .......(1)

at equilibrium,

Tension in string - force due acting on string due to net acceleration = pulling force applied by man.

or, T - ma' = ma

or, T - m√(a² + g²) = ma [from eq. 1]

or, T = m√(a² + g²) + ma

so, tension in the string is equal to, m√(a² + g²) + ma