Question

A highly rigid cubical block A of small mass M and side L is fixed
rigidly on another cubical block
B of same dimensions and of low modulus of rigidly n, such that the lower face of A completely
covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force
F is applied perpendicular to one of the side faces of A at the top. The side of B turns by an angle .
Now the whole arrangement is tumed upside down so that lower face of A is rigidly held to the
horizontal surface and we apply a small force F perpendicular to the side face B at the top. The side
of B now tums by an angle of ?​

Answer 1

Answer:

Modulus of rigidity η=

Aθ

F

Here, A=L

2

and θ=

L

x

for small θ

∴ Restoring force =F=−ηAθ

or acceleration, a=

m

F

=

M

ηL

xequation(1)

∵a∝(−x)

∴ Time period, T=2π

∣

∣

∣

∣

∣

∣

a

x

∣

∣

∣

∣

∣

∣

⟹T=2π

ηL

M