Question

A bob of mass m, suspended by a string of length `l_1` is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length `l_2`, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio `(l_1)/(l_2)` is
A. 1
B. 3
C. 5
D. `1//5`

Answer 1

Correct Answer - C
Velocity of the first bob at A = `sqrt(5gl_1)`
Velocity of the first bob at B=`sqrt(gl_1)`
At point B it collides elastically with another bob of same mass m suspended by a string of length `l_2` as shown in figure.
When two bodies of equal masses undergoes an elastic collision, their velocities are interchanged.
`therefore` Velocity of the second bob at B=`sqrt(gl_1)`
But to complete the vertical circle, the velocity of the second bob at B = `sqrt(5gl_2)`
`therefore sqrt(gl_1)=sqrt(5gl_2) " " or " " l_1/l_2=5`