Question

A particle of mass m starts from rest and moves in a circular path of radius R with a uniform angular acceleration α. The kinetic energy of the particle after n revolutions is

• A. nαmR²
• B. 2π nαmR²
• C. $\frac { 1 } { 2 }$mnαR²
• D. mnαR²

Answer 1

Answer: (B)

2π nαmR²

Answer 2

For uniform angular acceleration in a circular path, the angular speed is given by

ω² = $\omega _ { 0 } ^ { 2 } + 2 \alpha \theta$ = 0 + 2α (2πn)

kinetic energy of the particle

KE = $\frac { 1 } { 2 }$ m(Rω)² = $\frac { 1 } { 2 }$mR² (4απn) = 2πnm αR² , Hence, the correct choice is (2).