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A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2Rt2, where n is a constant. The power delivered to the particle by the force acting on it, is :
- a)1/2 Mn2R2t2
- b)Mn2R2t
- c)MnR2t2
- d)MnR2t
Correct answer is option 'B'. Can you explain this answer?
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A particle of mass M is moving in a circle of fixed radius R in such a...
Given, centripetal acceleration of the particle at time t is n^2Rt^2.
To find: Power delivered to the particle by the force acting on it.
Formula: Power = Force x Velocity
Force acting on the particle: F = ma (where a is the centripetal acceleration)
Using the given acceleration, we get:
F = m(n^2Rt^2)
The velocity of the particle v = ωR (where ω is the angular velocity)
Using the formula for centripetal acceleration, we get:
a = n^2R
ω = √(a/R) = n
v = nR
Now, power can be calculated as:
Power = F x v = m(n^2Rt^2) x nR
= Mn^2R^2t
Hence, the correct answer is option B.
To find: Power delivered to the particle by the force acting on it.
Formula: Power = Force x Velocity
Force acting on the particle: F = ma (where a is the centripetal acceleration)
Using the given acceleration, we get:
F = m(n^2Rt^2)
The velocity of the particle v = ωR (where ω is the angular velocity)
Using the formula for centripetal acceleration, we get:
a = n^2R
ω = √(a/R) = n
v = nR
Now, power can be calculated as:
Power = F x v = m(n^2Rt^2) x nR
= Mn^2R^2t
Hence, the correct answer is option B.
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A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2Rt2, where nis a constant. The power delivered to the particle by the force acting on it, is :a)1/2 Mn2R2t2b)Mn2R2tc)MnR2t2d)MnR2tCorrect answer is option 'B'. Can you explain this answer?
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