If 2× 105J of work is done in producing rotational kinetic energy of a wheel having moment of inertia of 10kg.m2 then the angular velocity (in rads- 1 ) acquired by the wheel is equal to

Question

If 2× 105J of work is done in producing rotational kinetic energy of a wheel having moment of inertia of 10kg.m2 then the angular velocity (in rads- 1 ) acquired by the wheel is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

From work-energy theorem, Work done produces change in kinetic energy, ∴ W=(1/2) I ω2 ldots .(∵ K . E .=(1/2) I ω2) ∴ ω =√(2 W/I)=√(2 × 2 × 105/10)=200rad/s

Q. If $2 \times 1 0^{5} J$ of work is done in producing rotational kinetic energy of a wheel having moment of inertia of $10 k g . m^{2}$ then the angular velocity (in $r a d s^{- 1}$ ) acquired by the wheel is equal to

From work-energy theorem,
Work done produces change in kinetic energy,
$∴ W = \frac{1}{2} I ω^{2} \dots . (∵ K . E . = \frac{1}{2} I ω^{2})$
$∴ ω = \frac{2 W}{I} = \frac{2 \times 2 \times 1 0 ^{5}}{10} = 200 r a d / s$

Q. If 2×105J of work is done in producing rotational kinetic energy of a wheel having moment of inertia of 10kg.m2 then the angular velocity (in rads−1 ) acquired by the wheel is equal to

From work-energy theorem, Work done produces change in kinetic energy, ∴W=21​Iω2….(∵K.E.=21​Iω2) ∴ω=I2W​​=102×2×105​​=200rad/s

Q. If $2 \times 1 0^{5} J$ of work is done in producing rotational kinetic energy of a wheel having moment of inertia of $10 k g . m^{2}$ then the angular velocity (in $r a d s^{- 1}$ ) acquired by the wheel is equal to

From work-energy theorem,
Work done produces change in kinetic energy,
$∴ W = \frac{1}{2} I ω^{2} \dots . (∵ K . E . = \frac{1}{2} I ω^{2})$
$∴ ω = \frac{2 W}{I} = \frac{2 \times 2 \times 1 0 ^{5}}{10} = 200 r a d / s$