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AP EAMCET202124 Aug 2021Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A force-time (F-t) graph for a linear motionis shown in following figure. The segments shown are circular. The linear momentum gained between 0 and 8 ~s is

Options

  1. A-2 N s
  2. B0
  3. C4 Ns
  4. D6 Ns

Correct answer

B. 0

Step-by-step solution

From graph, the force is varying sinusoidally with time by equation, F=-2 t ...(i) where, be the angular frequency of variation of force. Since, the graph is completing one cycle in 8 ~s , hence time period, T=8 ~s Using expression of change of momentum, p= ₀^8 F d t= ₀^8-2 t d t [from Eq. (i)] aligned & =- 2 [ t]₀^8 & = -2 [ 8- 0] aligned = -2 [ 2 8 8-0 ] ( = 2 T )= -2 [ 2 ]=0[ 0= 2 =0] Hence, the gain or change of linear momentum is zero.

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