Question

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k²rt², where k is a constant. The power delivered to the particle by the force acting on it is given as

• A. Zero
• B. mk²r²t²
• C. mk²r²t
• D. mk²rt

Answer 1

The Correct Option is C

The correct answer is (C) : mk²r²t
\(a_r = k²rt² = \frac{v²}{r}\)
\(⇒ v² = k²r²t² \) or   \( v = krt\)
and 
\(\frac{d |v|}{dt} = kr\)
\(⇒ a_t = kr\)
\(⇒ | \stackrel{→}{F} . \stackrel{→}{v} | = (mkr) ( krt)\)
\(= mk^2r^2t \)= power delivered