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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 n2R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :
- a)1/2 M n2R2t2
- b)M n2R2t
- c)M n R2t2
- d)M n R2t
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A particle of mass M is moving in a circle of fixed radius R in such ...
Centripetal acceleration ac = n2Rt2
View all questions of this test
ac = v2/R = n2Rt2
V2 = n2R2t2
v = nRt
ac = dv/dt = nR
Power = matv = m nR nRt = Mn2R2t
Most Upvoted Answer
A particle of mass M is moving in a circle of fixed radius R in such ...
Given:
- Mass of the particle, M
- Radius of the circle, R
- Centripetal acceleration at time t, n^2Rt^2
- Constant, n
To find:
The power delivered to the particle by the force acting on it.
Solution:
The power delivered to a particle is given by the equation:
Power = Force x Velocity
1. Finding the force:
The force acting on the particle is the centripetal force, which is given by the equation:
Force = Mass x Centripetal Acceleration
Substituting the given values, we have:
Force = M x n^2Rt^2
2. Finding the velocity:
The velocity of the particle moving in a circle can be found using the formula:
Velocity = 2πR/T
where T is the time period of one complete revolution.
The time period of one complete revolution can be found using the equation:
Centripetal Acceleration = 4π^2R/T^2
Substituting the given centripetal acceleration expression, we have:
n^2Rt^2 = 4π^2R/T^2
Simplifying the equation, we get:
T^2 = 4π^2/n^2
Taking square root on both sides, we have:
T = (2π/n)
Now, substituting this value of T in the velocity equation, we get:
Velocity = 2πR/(2π/n)
Velocity = nR
3. Calculating the power:
Now that we have the force and velocity, we can calculate the power using the equation:
Power = Force x Velocity
Substituting the values, we have:
Power = (M x n^2Rt^2) x (nR)
Power = Mn^2R^2t^2
Therefore, the power delivered to the particle by the force acting on it is Mn^2R^2t^2, which corresponds to option B.
- Mass of the particle, M
- Radius of the circle, R
- Centripetal acceleration at time t, n^2Rt^2
- Constant, n
To find:
The power delivered to the particle by the force acting on it.
Solution:
The power delivered to a particle is given by the equation:
Power = Force x Velocity
1. Finding the force:
The force acting on the particle is the centripetal force, which is given by the equation:
Force = Mass x Centripetal Acceleration
Substituting the given values, we have:
Force = M x n^2Rt^2
2. Finding the velocity:
The velocity of the particle moving in a circle can be found using the formula:
Velocity = 2πR/T
where T is the time period of one complete revolution.
The time period of one complete revolution can be found using the equation:
Centripetal Acceleration = 4π^2R/T^2
Substituting the given centripetal acceleration expression, we have:
n^2Rt^2 = 4π^2R/T^2
Simplifying the equation, we get:
T^2 = 4π^2/n^2
Taking square root on both sides, we have:
T = (2π/n)
Now, substituting this value of T in the velocity equation, we get:
Velocity = 2πR/(2π/n)
Velocity = nR
3. Calculating the power:
Now that we have the force and velocity, we can calculate the power using the equation:
Power = Force x Velocity
Substituting the values, we have:
Power = (M x n^2Rt^2) x (nR)
Power = Mn^2R^2t^2
Therefore, the power delivered to the particle by the force acting on it is Mn^2R^2t^2, which corresponds to 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 n2R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :a)1/2 M n2R2t2b)M n2R2tc)M n R2t2d)M n R2tCorrect answer is option 'B'. Can you explain this answer?
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