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)=sqrt(M(g)/mu)`
`implies (g^2+a^2)/(g)=((60.5)/60)^2`
`1+(1a^2)/(2g^2)=1+1/60` using by binomial approximation
`implies a = g/sqrt30 implies ` closest answer a = `g/5`