A body of mass 5 kg acquires an angular acceleration of 10 rad s-2 by an applied torque of 2 N m . Find its radius of gyration.

Question

A body of mass 5 kg acquires an angular acceleration of 10 rad s-2 by an applied torque of 2 N m . Find its radius of gyration. (A)  2.5 m  (B)  √2.5 m  (C)  √0.2 m  (D)  0.2 m

Tardigrade Admin · Accepted Answer

m=5 Kg, α=10 rad s-2, τ=2 N m Torque, τ=I α=mk2α (∵ I=mk2) where k is the radius of gyration ∴ 2=5× k2×10 or k2=0.04 or k=0.2 m

Q. A body of mass $5 k g$ acquires an angular acceleration of $10 r a d s^{- 2}$ by an applied torque of $2 N m$ . Find its radius of gyration.

$2.5 m$

$2.5 m$

$0.2 m$

$0.2 m$

$m = 5 K g$ ,
$α = 10$ rad $s^{- 2}$ ,
$τ = 2 N m$
Torque, $τ = I α = m k^{2} α (∵ I = m k^{2})$
where $k$ is the radius of gyration
$∴ 2 = 5 \times k^{2} \times 10$
or $k^{2} = 0.04$ or $k = 0.2 m$

Q. A body of mass 5kg acquires an angular acceleration of 10rads−2 by an applied torque of 2Nm . Find its radius of gyration.

2.5m

2.5​m

0.2​m

0.2m

m=5Kg, α=10 rad s−2, τ=2Nm Torque, τ=Iα=mk2α(∵I=mk2) where k is the radius of gyration ∴2=5×k2×10 or k2=0.04 or k=0.2m

Q. A body of mass $5 k g$ acquires an angular acceleration of $10 r a d s^{- 2}$ by an applied torque of $2 N m$ . Find its radius of gyration.

$2.5 m$

$2.5 m$

$0.2 m$

$0.2 m$

$m = 5 K g$ ,
$α = 10$ rad $s^{- 2}$ ,
$τ = 2 N m$
Torque, $τ = I α = m k^{2} α (∵ I = m k^{2})$
where $k$ is the radius of gyration
$∴ 2 = 5 \times k^{2} \times 10$
or $k^{2} = 0.04$ or $k = 0.2 m$