JEE PYQ: Mechanical Properties Of Fluids Question 26
Question 26 - 2019 (10 Apr 2019 Shift 2)
A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = $10^3$ kg/m$^3$]
(1) 46.3 kg
(2) 87.5 kg
(3) 65.4 kg
(4) 30.1 kg
Show Answer
Answer: (2) 87.5 kg
Solution
When a body floats then the weight of the body = upthrust $\therefore (50)^3 \times \frac{30}{100} \times (1) \times g = M_{\text{cube}} g$ …(i)
Let $m$ mass should be placed, then $(50)^3 \times (1) \times g = (M_{\text{cube}} + m)g$ …(ii)
Subtracting equation (i) from equation (ii): $\Rightarrow mg = (50)^3 \times g(1 - 0.3) = 125 \times 0.7 \times 10^3$ g
$\Rightarrow m = 87.5$ kg
BETA
