A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed 60 ~cm ⁻¹ on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is 66 ~cm ⁻¹ . The acceleration of the car is nearly (g=10 ~ms ⁻² )

Step-by-step solution

When car is at rest, tension in string is T=m g . aligned T & =M g=m v₁^2 V₁= T r & = M g &..(i) aligned When car is accelerating tension, aligned T & = M (a^2+g^2 )^ 1 / 2 v₂ & = M (a^2+g^2 )^ 1 / 2 aligned Dividing Eq (i) by Eq. (ii), we get gathered v₂ v₁ = M (a^2+g^2 )^ 1 / 2 M g = 66 60 (a^2+g^2 )^ 1 / 2 g = 121 100 gathered Squaring, we get array rlrl & & a^2+g^2 & = ( 121 100 )^2 & a^2 & =146.41-100 & a^2 & =46.41 array So, a=6.8 ~ms ⁻²