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QJEEM21Ph18c4: JEE Main 2021 Physics - Class 11 JEEM21Ph18c4 Solution: A body of mass M moving at speed V 0 collides elastically with…

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 θ\theta 1 and θ\theta 2 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 θ\theta 1 and θ\theta 2 will be equal, is :

Multiple Choice Options

  • A 4
  • B 1
  • C 3
  • D 2

Step-by-Step Verified Solution

JEE Main 2021 (Online) 31st August Morning Shift Physics - Center of Mass and Collision Question 43 English Explanation
Given θ\theta 1 = θ\theta 2 = θ\theta

from momentum conservation

in x-direction MV0 = MV1 cos θ\theta + mV2 cos θ\theta

in y-direction 0 = MV1 sin θ\theta −- mV2 sin θ\theta

Solving above equations

V2=MV1m{V_2} = {{M{V_1}} \over m} , V0 = 2V1 cos θ\theta

From energy conservation

12MV02=12MV12+12MV22{1 \over 2}MV_0^2 = {1 \over 2}MV_1^2 + {1 \over 2}MV_2^2

Substituting value of V2 & V0, we will get

Mm+1=4cos⁡2θ≤4{M \over m} + 1 = 4{\cos ^2}\theta \le 4

Mm≤3{M \over m} \le 3

Option (c)

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