A block weighing 600 N is placed between the hands using a compressive force of 750 N as shown in the figure. What should be the coefficient of friction between hands and the block to prevent slipping?

The correct answer is option 1) i.e. 0.40

CONCEPT:

• Friction: The frictional force is a force that opposes the relative motion of an object.
  • The force acts when two surfaces in contact are moving past one another or when one surface is moving past a stationary surface.
  • The frictional force Ff exerted by a surface on an object is given by

⇒ Ff = μN

Where μ is the coefficient of friction and N is the normal force exerted on the object by the surface.

CALCULATION:

• Slipping off the block occurs if the weight of the block exceeds the frictional force exerted between the hands and the block.
• Therefore, to prevent slipping the weight of the block must be balanced by the frictional forces.

From the figure, the weight of the book acts downwards and the friction between the hand and block acts upwards to oppose slipping.

• The compressive force applied will be equivalent to the normal force N exerted by the block on the hand.

Therefore,

⇒ F_f + Ff = W

⇒ 2F_f = 600 ⇒ 2μN = 600

• Coefficient of friction, 

\(⇒\mu = \frac{600}{2N} = \frac{600}{2\times750} = 0.4\)