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

`V = sqrt((T)/(mu)) rArr (DeltaV)/(V)= (1)/(2)(DeltaT)/(T) , (0.5)/(60)=(1)/(2) (msqrt(g^(2) + a^(2) - mg))/(mg) rArr (1)/(60)=(1+(a^(2))/(g^(2)))^(1//2) -1`
`rArr (1)/(60) = 1+(1)/(2)(a^(2))/(g^(2))-1 rArr a=(g)/(sqrt30)=(g)/(5.47)`