Question

28. A torque of 36 Nm, produces an angular
acceleration of 9 rad/s2 in a body. If the radius of
gyration of the body is 4 m, then the mass of the
body is
(1) 0.125 kg
(2) 4 kg
(3) 1 kg
(4) 0.25 kg
Space for R​

Answer 1

Mass of the body$m = \textrm{0.250 Kg} = \textrm{250 gram}$

Explanation:

Given that,

Torque $= \textrm{36 Nm}$

Angular acceleration $\alpha = 9 \frac{rad}{m^{2}}$

Radius Of Gyration $k = \textrm{4 m}$  

As we know that,

Torque $=$ Moment of Inertia $\times$ Angular acceleration

Here, Moment of Inertia $=$ Mass $\times$ (Radius Of Gyration)²

So, $mk^{2} \times \alpha = Torque$

$m =\frac{36}{9\times 4^{2}}$

Mass of the body $m = \textrm{0.250 Kg} = \textrm{250 gram}$.