Asmall sphere hangs from a string attached to the ceiling of a uniformly accelerating train car. it is observed that the string makes an angle of 37° with respect to the vertical. the magnitude of the acceleration a of the train car is most nearly

a= 7.53 m/s²

Explanation:

Given that

Angle made by small sphere from vertical ,θ = 37°

Lets take acceleration of the car is a m/s²

Leta take mass of the sphere = m

Gravity force = mg

Tension in the string = T

Vertical component = T cos θ

Horizontal component = T sin θ

From second law of Newton's

T cos θ= m a -----1

By balancing force in vertical direction

T sin θ = m g   -2

From 1  and 2

a = g tan37°              ( take g=10 m/s²)

a= 10  tan37°        

a= 7.53 m/s²