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Two particles, each of mass m, are conne...

Two particles, each of mass m, are connected by a light inextensible string of lenthe `2l`. Initially they lie on a smooth horizontal table at points A and B distant `l` apart. The particle at A is projected across the table with velocity u. Find the speed with which the second particle begins to move if the direction of u is :-
(i) along BA.
(ii) at an angle of `120^(@)` with AB
(iii) perpendicular to AB. In each case calculate (in teerms of m and u) the impulsive tension in the string.

Text Solution

Verified by Experts

The correct Answer is:
(i) `(u)/(2), (m u)/(2)` (ii) `(usqrt3)/(8), (m u sqrt13)/(8)` (iii) `(usqrt3)/(4), (m u sqrt3)/(4)`
(a) `m u - T Deltat = mv` …..(i)
`T Deltat = mv` …..(ii)
On solving eq. (i) & (ii)

(b) `(2l)/(sin 120^(@)) = (l)/(sin theta)`
`sin theta = (sqrt3)/(4), cos theta = (sqrt13)/(4)`
`m u cos theta - T Deltat = mv` ...(i)
`rArr T Deltat = mv` ...(ii)
On solving eq. (i) & (ii) `(u cos theta)/(2) = v`

(c ) `2l cos theta = l rArr theta = 60^(@)`
`m u cos 30^(@) - T Deltat = mv` ...(i)
`T Deltat = (m u sqrt3)/(4)` ....(ii)
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