A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of `60 cm s^-1` on the string when the car is at rest and `62 cm s^-1` when the car accelerates on a horizontal road. Find the acceleration of the car. Take `g = 10 ms^-2`

Answer

B, C

Explanation

Let M=mass of the heavy ball
m=mass per unit length
`wave speed v_1=sqrt((T/m))=sqrt((Mg/m))`
(because T=Mg)`
`rarr 60 =sqrt((Mg/m))`
`rarr (Mg)/m=(60)^2` …………i
Again `v_2=sqrt((T/m))`
`rarr v_2=([(Ma)^2+(Mg)^2]^(1/4))/m^(1/2)`
`rarr v_2=([(Ma)^2+(Mg)^2]^(1/4))/m^(1/2)`
`=62`
`rarr (sqrt([(Ma)^2+(Mg)^2])/m=(62)^3.............2
eqn 1 + Eqn 2
` gt ((Mg)/m)xxm/(sqrt(Ma)^2+(Mg)^2)=(60/62)^2` `=360/3844`
`g/(sqrt(a^2+g^2))=0.936`
`g^2/((a^2+g^2)=0.876`
`rarr (a^2+100)0.86=100`
`rarr a^2=12.4/0.867=14.15`
`rarr a=3.76=3.7m/s^2`
`:. Acceleration of car =3.7m/s^2`