When the temperature of a rod increases from t to t+Δt, its moment of inertia about a perpendicular axis passing through its centre increases from I to I+ΔI. If α be the coefficient of linear expansion of the rod, then the value of ΔII is
A
2αΔt
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
αΔt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3αΔt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4αΔt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A2αΔt Given:
Temperature change =Δt
Change in moment of inertia =ΔI
Coefficient of linear expansion of the rod =α
To find:
Ratio, ΔII=?
We know that, moment of inertia of a rod about a perpendicular axis passing through its centre is given by I=mL212 ........(1)
where m is mass and L is the length of the rod.
Differentiating w.r.t. L, we get dIdL=112×2mL ⇒ΔI=2×112×mLΔL ⇒ΔI=2×112m×L2L×ΔL=2IΔLL
[ from (1) ] ⇒ΔI=2IαLΔTL
[ from formula of linear expansion ] ⇒ΔII=2αΔT