A heavy ball is mass M is suspended from the ceiling of a car by a light string of mass `m(m lt lt M)`. When the car is at rest, the speed of transverse waves in the string is `60ms^(-1)`. When the car has acceleration a, the wave-speed increases to `60.5ms^(-1)`. The value of a, in terms of gravitational acceleration g, is closest to:

Options

A. `(g)/(30)`
B. `(g)/(20)`
C. `(g)/(5)`
D. `(g)/(10)`

Answer

C

Explanation

Speed of wave in string is `upsilon.mu` = mass of string per unit length.
`upsilon = sqrt((T)/(mu)) = sqrt((Mg)/(mu))" "because` when car at rest
when car is in motion having acceleration is a
`upsilon' = sqrt((T')/(mu)) = sqrt((Mg')/(mu))= sqrt((M(sqrt(g^(2) + a^(2))))/(mu))`
`(upsilon)/(upsilon') = sqrt((g)/(sqrt(g^(2) + a^(2)))) = ((60)/(60.5))`
`a = (g)/(5)`