A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical body o f mass m with horizontal velocity V=√2gl, the tension in the string increases just after striking by

Question

A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical body o f mass m with horizontal velocity V=√2gl, the tension in the string increases just after striking by (A) mg (B) 3 mg (C) 2 mg (D) None o f these

Tardigrade Admin · Accepted Answer

m vo=(m +m) v v =(vo/2) T =(2 m v2/l)+2 m g T =(2 m v02/4 l)+2 m g =(m(2 g l)/2 l)+2 m g T =3 m g Increase in tension =3 mg - mg =2 mg

Q. A body is hanging from a rigid support by an inextensible string of length $l$ . It is struck inelastically by an identical body o f mass $m$ with horizontal velocity $V = 2 g l$ , the tension in the string increases just after striking by

mg

3 mg

2 mg

None o f these

$m v_{o} = (m + m) v$
$v = \frac{v _{o}}{2}$
$T = \frac{2 m v ^{2}}{l} + 2 m g$
$T = \frac{2 m v _{0}^{2}}{4 l} + 2 m g$
$= \frac{m ( 2 g l )}{2 l} + 2 m g$
$T = 3 m g$
Increase in tension $= 3 m g - m g = 2 m g$

Q. A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical body o f mass m with horizontal velocity V=2gl​, the tension in the string increases just after striking by

mg

3 mg

2 mg

None o f these

mvo​=(m+m)v v=2vo​​ T=l2mv2​+2mg T=4l2mv02​​+2mg =2lm(2gl)​+2mg T=3mg Increase in tension =3mg−mg=2mg

Q. A body is hanging from a rigid support by an inextensible string of length $l$ . It is struck inelastically by an identical body o f mass $m$ with horizontal velocity $V = 2 g l$ , the tension in the string increases just after striking by

$m v_{o} = (m + m) v$
$v = \frac{v _{o}}{2}$
$T = \frac{2 m v ^{2}}{l} + 2 m g$
$T = \frac{2 m v _{0}^{2}}{4 l} + 2 m g$
$= \frac{m ( 2 g l )}{2 l} + 2 m g$
$T = 3 m g$
Increase in tension $= 3 m g - m g = 2 m g$