Question:
A cubical block of side \(0.5\ \mathrm{m}\) 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 \(=10^{3}\ \mathrm{kg/m^3}\)]
A cubical block of side \(0.5\ \mathrm{m}\) 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 \(=10^{3}\ \mathrm{kg/m^3}\)]
Show Hint
At the limit the block is fully submerged, so the extra load equals the extra buoyant force.
Updated On: Nov 5, 2026
- \(30.1\ \mathrm{kg}\)
- \(87.5\ \mathrm{kg}\)
- \(65.4\ \mathrm{kg}\)
- \(46.3\ \mathrm{kg}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Volume \(V=0.5^3=0.125\ \mathrm{m^3}\).
Floating with 30% submerged: \(m_{block}g=0.3V\rho g\Rightarrow m_{block}=0.3\times0.125\times10^{3}=37.5\ \mathrm{kg}\).
Just fully submerged: \((m_{block}+m)g=V\rho g\Rightarrow m_{block}+m=125\ \mathrm{kg}\).
\(m=125-37.5=87.5\ \mathrm{kg}\).
Answer: (2) 87.5 kg
Floating with 30% submerged: \(m_{block}g=0.3V\rho g\Rightarrow m_{block}=0.3\times0.125\times10^{3}=37.5\ \mathrm{kg}\).
Just fully submerged: \((m_{block}+m)g=V\rho g\Rightarrow m_{block}+m=125\ \mathrm{kg}\).
\(m=125-37.5=87.5\ \mathrm{kg}\).
Answer: (2) 87.5 kg
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main Fluid Mechanics Questions
- In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms–1 and 65 ms–1 respectively. If the wing area is 2 m2 the lift of the wing is _______ N.
(Given density of air = 1.2 kg m-3) - A plane is in level flight at constant speed and each of its two wings has an area of 40 m2 . If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is ________kg. (Take air density to be 1 kg m–3 and g = 10 ms–2
- Given below are two statements:
Statement I: When the speed of liquid is zero everywhere, the pressure difference at any two points depends on the equation $$ P_1 - P_2 = \rho g (h_2 - h_1). $$ Statement II: In the ventury tube shown, $$ 2gh = v_1^2 - v_2^2. $$
In the light of the above statements, choose the most appropriate answer from the options given below. - Given below are two statements :
Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be 0°.
Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement.
Choose the correct answer from the options given below. - A sphere of relative density \( \sigma \) and diameter \( D \) has a concentric cavity of diameter \( d \). The ratio of \( \frac{D}{d} \), if it just floats on water in a tank, is:
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions