Question

A block A kept on an inclined surface just begins to slide if the inclination is ${30}^{\circ }$. The block is replaced by another block B and it is found that it just begins to slide if the inclination is ${40}^{\circ }$.

• A. mass of A > mass of B
• B. mass of A < mass of B
• C. mass of A = mass of B
• D. all the three are possible

Answer 1

The correct option is D

all the three are possible

Let's take a block of mass $m_A$ and see

Since the block is just about to slide so limiting friction

fr = ${\mu }_A$N

N = $m_A$g cos ${30}^{\circ }$

fr = $m_A$$m_A$ g cos ${30}^{\circ }$

for the block to slide down the incline

$m_A$ sin ${30}^{\circ }$ $\ge$ ${\mu }_A$$m_A$ g cos ${30}^{\circ }$

So condition for slipping is tan ${30}^{\circ }$ $\ge$ ${\mu }_A$ oh wow it doesn't at all depend upon the mass of the block so doesn't matter what mass you keep until my condition is satisfied the block has to slip similarly for block B i.e. ${30}^{\circ }$ $\ge$ ${\mu }_B$

So slipping only depends upon $\mu$ (type of materials in contact) and not the mass of A or B.