A cube having a side of 10 cm with unknown mass and 200 gm mass w… - Vidyadip

Question

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm . Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is $1 \mathrm{gm} / \mathrm{cm}^{3}$.) The unknown mass is _______________ kg.

✓

Answer

Given, volume of block $=\left(10 \times 10^{-2}\right)^{3}=10^{-3} \mathrm{~m}^{3}$
Let density of block $=\rho \mathrm\ {kg} / \mathrm{m}^{3}$
mass of block $=\rho \times 10^{-3} \mathrm{~kg}$
Buoyant Force $\left(F_{B}\right)=1000 \times \frac{10^{-3}}{2} \times 10=5 \mathrm{~N}$
F.B.D. of blocks

Balancing torque about point O , we get
$\operatorname{mg}\left(2 \times 10^{-2}\right)-\mathrm{F}_{\mathrm{B}}\left(2 \times 10^{-2}\right)=0.2 \mathrm{~g}\left(25 \times 10^{-2}\right)$
$\rho \times 10^{-3} \times 10 \times 2-10=50$
$\rho=3000 \mathrm{~kg} / \mathrm{m}^{3}$
Hence, mass of block $=\rho \times 10^{-3}$
$=3000 \times 10^{-3}=3 \mathrm{~kg}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "SECTION - B [PHYSICS - NUMERIC]" from JEE Main 8-April-2025 Paper - Shift 2→JEE Main 8-April-2025 Paper - Shift 2 — all question types→JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The power dissipated in the circuit shown in the figure is $30\, Watts$. The value of $R$ is ............. $\Omega$

A series $LCR$ circuit is designed to resonate at an angular frequency $\omega_{0}=10^{5} \,rad / s$. The circuit draws $16\, W$ power from $120\, V$ source at resonance. The value of resistance $'R'$ in the circuit is ...... $\Omega$.

A Carnot engine has an efficiency of $50 \%$ when its source is at a temperature $327^{\circ}\,C$. The temperature of the sink is $.........^{\circ} C$

A metal is heated in a furnace where a sensor is kept above the me al surface to read the power radiated $(P)$ by the metal. The sensor has a scale that displays $\log _{\text {: }}\left(P / P_0\right)$, where $P_0$ is a constant. When the metal surface is at a temperature of $487^{\circ} \mathrm{C}$, the sensor shows a value $1$. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $2767^{\circ} \mathrm{C}$ ?

An electron beam is moving between two parallel plates having electric field $1.125 \times {10^{ - 6}}N/m$. A magnetic field $3 \times {10^{ - 10}}T$ is also applied so that beam of electrons do not deflect. The velocity of the electron is ............ $m/s$

If the length of the simple pendulum is increased by $44\%$, then what is the change in time period of pendulum ..... $\%$

A body of mass $2\, kg$ travels according to law $x = at + bt^2 + ct^3$, where $a = 3\, m/s$, $b = 4\,m/s^2$ and $c = 5\, m/s^3$, then force acting on body at $t = 2\, s$ ......... $N$.

Two concentric circular coils, $C _{1}$ and $C _{2}$, are placed in the $XY$ plane. $C _{1}$ has $500$ turns, and a radius of $1\; cm . C _{2}$ has $200$ turns and radius of $20\, cm . C _{2}$ carries a time dependent current $I(t)=\left(5 t^{2}-2 t+3\right) \;A$ where $t$ is in $s$. The $emf$ nduced in $C _{1}$ (in $mV$ ), at the instant $t =1\; s$ is $\frac{4}{ x }$. The value of $x$ is

Light of wavelength is $7200 Å$ in air. It has a wavelength in glass ($\mu = 1.5$) equal to.......$\mathop A\limits^o $

A ray of light passing through a prism $(\mu=\sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)