Question

1. Two blocks of mass M-6 kg and m = 3 kg are
placed as shown in the figure. Coefficient of friction
between M and m is 0.5. Coefficicnt of friction be-
tween M and the surface is 0.4. The maximum hori-
zontal force that can be applied to the mass M so that
they move without separation is: (g = 10 ms)
a) 41 N b) 61 N
c) 81 N d) 101 N
ke rest on​

Answer 1

Here, ω=

3m

k

Maximum static frictional force, $$f_{max}=\mu\,

mg\,cos\,\theta=2\,tan\,\theta\,mg\,cos\,\theta=2\,mg\,cos\,\theta$$

Applying Newton's second law on the block at lower extreme position, we get

f−mgcosθ=mω

2

A

⟹f=mω

2

A+mgsinθ

As f≤f

max

,

ω

2

A=gsinθ

or

Amplitude, A=

k

3mgsinθ