Question

. A simple pendulum of length land having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?

Answer 1

The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car. 
Acceleration due to gravity = g 
Centripetal acceleration = v2/R
where,
v is the uniform speed of the car
R is the radius of the track
Effective acceleration (g') is given as:  

Answer 2

Answer:

The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car.

Acceleration due to gravity =g

Centripetal acceleration =v

2

/R

where,

v is the uniform speed of the car

R is the radius of the track

Effective acceleration (g

′

) is given as:

g

′

=

g

2

+

R

2

v

4

∴ Time peroid, t=2π

g

′

l

=2π

g

2

+

R

2

v

4

l