The total kinetic energy of a body of mass 10 kg and radius 2 m moving with a velocity of 15 m / s without slipping is 40 joule. The radius of gyration is

Question

The total kinetic energy of a body of mass 10 kg and radius 2 m moving with a velocity of 15 m / s without slipping is 40 joule. The radius of gyration is (A) 1 m (B) 2 m (C) 1.89 m (D) 1.71 m

Tardigrade Admin · Accepted Answer

Total kinetic energy of the body is (1/2) m v2(1+(K2/R2)) 40=(1/2) × 10 ×(15)2(1+(K2/(2)2)) (80/10 × 225)=1+(K2/4) =0.96 × 4=K2 K=1.89 m

Q. The total kinetic energy of a body of mass $10 k g$ and radius $2 m$ moving with a velocity of $15 m / s$ without slipping is 40 joule. The radius of gyration is

$1 m$

$2 m$

$1.89 m$

$1.71 m$

Total kinetic energy of the body is $\frac{1}{2} m v^{2} (1 + \frac{K ^{2}}{R ^{2}})$
$40 = \frac{1}{2} \times 10 \times (15)^{2} (1 + \frac{K ^{2}}{( 2 ) ^{2}})$
$\frac{80}{10 \times 225} = 1 + \frac{K ^{2}}{4}$
$= 0.96 \times 4 = K^{2}$
$K = 1.89 m$

Q. The total kinetic energy of a body of mass 10kg and radius 2m moving with a velocity of 15m/s without slipping is 40 joule. The radius of gyration is

1m

2m

1.89m

1.71m