Question

A wooden block of mass 60 kg and dimensions $30cm\times 40cm\times 50cm$ is kept on horizontal floor. If $P_1$ is the maximum pressure exerted on the floor by the block and $P_2$ is the minimum pressure exerted on the floor by the block, then

• A.
  $3P_1=5P_2$
• B.
  $5P_1=3P_2$
• C.
  $3P_1=8P_2$
• D.
  $P_1=3P_2$

Answer 1

The correct option is A

$3P_1=5P_2$
Mass of the block = 60 kg

Weight of the block, $F=mg=60\times 10=600N(Usingg=10m/s^2)$



Pressure exerted by the block when it is made to lie on the dimensions $50cm\times 40cm:$ $P_A=\frac{F}{A_1}=\frac{mg}{50\times 40}=\frac{600}{50\times 40}=0.3N/c{m}^2$

Pressure exerted by the block when it is made to lie on the dimensions $40cm\times 30cm:$
$P_B=\frac{F}{A_2}=\frac{600}{40\times 30}=0.5N/c{m}^2$

Pressure exerted by the block when it is made to lie on the dimensions $50cm\times 30cm:$


$P_c=\frac{F}{A_3}=\frac{600}{50\times 30}=04N/c{m}^2$

Maximum pressure, $P_B=0.5N/c{m}^2=P_1$
Minimum pressure, $P_A=0.3N/c{m}^2=P_2\Rightarrow \frac{P_1}{P_2}=\frac{0.5}{0.3}\Rightarrow 3P_1=5P_2$

Hence, the correct answer is option (a).