Equilibrium based Questions

Question 1:
A uniform chain of mass m and length l is lying on a horizontal table with one third of its length hanging over the edge of the table. If the chain is in limiting equilibrium what is the coefficient of friction for the contact between the table and chain?

1/3

2/3

3/4

1/2

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Solution:

The hanging part of the chain has weight

$W_h = \frac{m}{3} g$

, and the part on the table has normal force

$N = \frac{2m}{3} g$

. In limiting equilibrium, friction

$F_f = \mu N$

balances

$W_h$

, so

$\mu \times \frac{2m}{3} g = \frac{m}{3} g$

Solving,

$\mu = \frac{1}{2}$

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Question 2:
In the arrangement shown, the normal reaction between the block A and ground is:

10 N

20 N

30 N

40 N

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Solution:

Weight of block $A$ = $4 \times 10 = 40$ N.

Weight of block $B$ = $2 \times 10 = 20$ N.

Tension in the string $T$ = Weight of $B$ = 20 N.

Normal reaction on $A$ , $N =$ Weight of $A$ – Tension $T$ = $40 - 20 = 20$ N.

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Question 3:
In translatory equilibrium

The net external force acting on particle is zero

The net external force acting on particle is constant (non-zero)

Particle is always at rest

Velocity of particle changes linearly with time

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Solution:

In translational equilibrium the net force acting on the object is zero. so the object moves with constant velocity.

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