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Question

Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius 4 m. If its speed is increasing at 3 m/s every second, at an instant when the speed of the particle is 4 m/s.

A
37
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B
53
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C
60
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D
45
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Solution

The correct option is B 53
Let the tangential acceleration be at
And centripetal acceleration be ac

Given the speed of the particle is v=4 m/s.
speed is increasing at 3 m/s every second at=dvdt=31=3 m/s2

Centripetal acceleration
ac=v2R=424=4 m/s2



Net acceleration,
anet=a2c+a2t=42+32=5 m/s2
Now angle between net acceleration and tangential acceleration is cosθ=atanet=35
θ=53

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