Rotational MotionHard
Question
A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2 ) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :
Options
A.more than 3 but less than 6
B.more than 6 but less than 9
C.more than 9
D.less than 3
Solution
r × F = I × α
2(20t - 5t2) = 10α ⇒ α = 4t - t2
= 4t - t2
dϖ = (4t - t2) dt
ϖ = 2t 2 -
(on integration)
ϖ = 0 ⇒ t = 6 s
ϖ =
= 2t2 -
⇒
(on integration)
θ (in 6 s) = 36 rad
⇒ 2πn = 36
2(20t - 5t2) = 10α ⇒ α = 4t - t2
= 4t - t2 dϖ = (4t - t2) dt
ϖ = 2t 2 -
(on integration)ϖ = 0 ⇒ t = 6 s
ϖ =
= 2t2 - ⇒
(on integration)θ (in 6 s) = 36 rad
⇒ 2πn = 36
Create a free account to view solution
View Solution FreeMore Rotational Motion Questions
A thin uniform rod of mass m and length l is free to rotate about its upper end. When it is at rest, it receives an impu...Figure shows a uniform disk, with mass M = 2.4 kg and radius R = 20 cm, mounted on a fixed horizontal axle. A block of m...Calculate the torque about point O in given diagram...Find minimum height of obstacle so that the sphere can stay in equilibrium...A particle of mass m and radius of gyration K is rotating with an angular acceleration α. The torque acting on the ...