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22/01/2022 2:19 pm
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A body of mass M moving at speed V0 collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles θ1 and θ2 with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles θ1 and θ2 will be equal, is
(1) 4
(2) 1
(3) 3
(4) 2
1 Answer
1
22/01/2022 2:26 pm
Correct answer: (3) 3
Explanation:
Given θ1= θ2 = θ
from momentum conservation in x-direction
MV0 = MV1 cosθ + mV2 cosθ
in y-direction 0 = MV1 sinθ - mV2 sinθ
Solving above equations
V2 = \(\frac{MV_1}{m}\), V0 = 2V1 cosθ
From energy conservation
\(\frac{1}{2}MV_0^2\) = \(\frac{1}{2}MV_1^2\) + \(\frac{1}{2}MV_2^2\)
Substituting value of V2 & V0, we will get
\(\frac{M}{m}\) + 1 = 4cos2θ ≤ 4
\(\frac{M}{m}\) ≤ 3