When the angular velocity of a uniformly rotating body has increased thrice, the resultant of force applied to it increases by 60 newton. Find the acceleration of the body in two cases. The mass of the body, m = 3 kg

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$2 \cdot 5 m / s^{2}, 7 \cdot 5 m / s^{2}$

$5 m / s^{2}, 45 m / s^{2}$

$2 \cdot 5 m / s^{2}, 22 \cdot 5 m / s^{2}$

$7 \cdot 5 m / s^{2}, 22 \cdot 5 m / s^{2}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given, $F_{1} = {mrω}_{0}^{2}$

and $F_{2} = mr {(3 ω_{0})}^{2}$

$∴ ΔF = F_{2} - F_{1} = mr [9 ω_{0}^{2} - ω_{0}^{2}] = 8 {mrω}_{0}^{2}$

$\Rightarrow 60 = 8 \times 3 \times {rω}_{0}^{2}$ or, ${rω}_{0}^{2} = (60 / 24)$

Now $a_{1} = {rω}_{0}^{2} = 60 / 24 = 2 \cdot 5 m / s^{2}$

and $a_{2} = 9 {rω}_{0}^{2} = 9 \times 2 \cdot 5 = 22 \cdot 5 m / s^{2}$

Watch 3-min video & get full concept clarity