Two particles A and B of mass `2m` and m respectively are attached to the ends of a light inextensible string of length `4a` which passes over a small smooth peg at a height `3a` from an inelastic table. The system is released from rest with each particle at a height a from the table. Find -
(i) The speed of B when A strikes the table
(ii) The time that elapses begore A first hits the table.
(iii) The time for which A is resting on the table after the first collision & begore it is first jerked off.

Answer

(i) `sqrt(2ag)/(3)` (ii) `(3v)/(g)` (iii) `(2v)/(g)`

Explanation

`2mg - T = 2m.a` ….(i)
`T - mg = m.a` ….(ii)
On solving eq. (i) & (ii) `a = (g)/(3)`
(a) `v_(B) = sqrt(u^(2) + 2as) = sqrt(0 + 2((g)/(3))a) = sqrt((2ag)/(3))`
(b) `s = ut + (1)/(2) t^(2), a = 0 + (1)/(2)((g)/(3)) t^(2), t = sqrt((6a)/(g)) = (3v)/(g)`
(c ) `t = (2v)/(g)`