KCET 2025 Physics Paper

A wooden block of mass M rests on a rough floor, while another block of the same mass is suspended from a point O by strings. To maintain equilibrium, we need to determine the coefficient of static friction between the block on the floor and the floor itself.
From the figure and given conditions, we can use the following equations for equilibrium:
The vertical component of tension:
Tsin‌θ=Mg‌‌...(i)
This equation accounts for the vertical force balance, where T is the tension in the string, and θ is the angle made by the string with the vertical.
The horizontal component of tension:
T‌cos‌θ=µMg‌‌...(ii)
Here, µ represents the coefficient of static friction.
To find µ, divide equation (ii) by equation (i):
‌‌

T‌cos‌θ

Tsin‌θ

=‌

µMg

Mg

‌cot‌θ=µ
Therefore, the coefficient of static friction is:
µ=cot‌θ