Home
Class 12
PHYSICS
A particle of mass m moves along a circu...

A particle of mass m moves along a circular path of radius r with a centripetal acceleration `a_n` changing with time t as `a_n=kt^2`, where k is a positive constant. The average power developed by all the forces acting on the particle during the first `t_0` seconds is

A

`(mrk^4)/(t_(0)^(2))`

B

`(mkrt_(0)^(2))/(2)`

C

`(mrkt_(0)^(2))/(8)`

D

`mrk^(4) t_(0)^(2))/(16)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `a_(n) = kt^(2)`
or `(v^2)/( r) = kt^(2)` or `v^(2) = krt^(2)`
Therefore, average power delivered `=("Total work done")/("Total time elapsed")`
Or `lt P gt =((1)/(2) m(v^(2)-0^(2) ) )/( t_(0)) = (m)/(2) (krt_(0)^(2))/(t_(0)) = (mkrt_(0)^(2))/( 2)`.
Promotional Banner

Topper's Solved these Questions

  • WORK, POWER, ENERGY

    MTG-WBJEE|Exercise EXERCISE (WB JEE WORKOUT) CATEGORY 3 : One or More than One Option Correct Type (2 Marks)|10 Videos

  • WORK, POWER, ENERGY

    MTG-WBJEE|Exercise EXERCISE (WB JEE Previous Years Questions) CATEGORY 1 : Single Option Correct Type (1 Mark)|3 Videos

  • WORK, POWER, ENERGY

    MTG-WBJEE|Exercise EXERCISE (WB JEE Previous Years Questions) CATEGORY 1 : Single Option Correct Type (1 Mark)|3 Videos

  • WAVE OPTICS

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTION (MCQ.s)|9 Videos

Similar Questions

Explore conceptually related problems

A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as a_(N)=kt^(2) where k is a constant. Find the time dependence of power developed by all the forces acting on the particle and the mean value of this power averaged over the first t seconds after the beginning of the motion.

A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as a_(n) = bt^(2) , where b is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first 2 seconds after the beginning of motion, (m = 1,v = 2,r = 1) .

A paricle of mass m moves along a circle of radius R with a normal acceleration varying with time as w_n=at^2 , where a is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first t seconds after the beginning of motion.

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a_(c) is varying with time t as a_(c) = k^(2)rt^(2) , where k is a constant. The power delivered to the particle by the forces acting on it is :

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a_(c) is varying with the time t as a_(c)=k^(2)r^(3)t^(4) where k is a constant. The power delivered to the particle by the forces acting on it is

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as a_c = k^2rt^2 , where k is a constant. Calculate the power delivered to the particle by the force acting on it.

A particle of mass m impves along a horzontal circle of radius R such that normal acceleration of particle varies with time as a_(n)=kt^(2). where k is a constant. Power developed by total at time t is

A particle of mass m is moving in a circular path of constant radius r , such that its centripetal force F_r varies with time t as F_r=K^2rt^2 , where k is a constant. What is the power delivered to the particle by the forces acting on it?