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Question

A small bob of mass m is suspended by a massless string from a cart of the same mass m as shown in the figure. The friction between the cart and horizontal ground is negligible. The bob is given a velocity v0 in horizontal direction as shown. The maximum height attained by the bob is
(initially whole system (bob+string+cart) was at rest).

A
2v20g
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B
v20g
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C
v204g
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D
v202g
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Solution

The correct option is C v204g
When ball reaches maximum height, let velocity of system (bob+string+cart) be v
By linear momentum conservation in horizontal direction,
for (bob+string+cart)
mv0=(m+m)v
v=v02
By mechanical energy conservation for (bob+string+cart)
12mv20+0+0=12(m+m)v2+mgh+0
12mv2012(2m)v204=mgh
Solving it,
h=v204g

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