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Question

Figure shows (x,t),(y,t) diagram of a particle moving in 2dimensions.

If the particle has a mass of 500 g, the force acting on the particle is (Assume x=t,y=t2 are equation of given graphs)

A
1 N along y axis
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B
1 N along x axis
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C
0.5 N along x axis
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D
0.5 N along y axis
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Solution

The correct option is A 1 N along y axis
Since the graph between x and t is a straight line and passing through the origin.
x=t
Since the graph between y and t is a parabola.
y=t2
vx=dxdt=1 and ax=dvxdt=0.
Since ax=0, force along x direction will be zero.
vy=dydt=2t and ay=2 ms2
The force acting on the particle is F=may=(0.5 kg)(2 ms2)=1 N along y axis

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