A thin uniform cylindrical shell, closed at both ends, is partial… - Vidyadip

MCQ

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_0$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

✓
more than half filled if $\rho_c$ is less than $0.5$
B
more than half filled if $\rho_c$ is less than $1.0$
C
half filled if $\rho_c$ is less than $0.5$
D
less than half filled if $\rho_c$ is less than $0.5$

✓

Answer

Correct option: A.

more than half filled if $\rho_c$ is less than $0.5$

a
Let outer volume of shell is $V_0$

Let inner volume of shell is $V_1$

Let volume of water inside the shall is $v$.

$\Rightarrow 1 Vg +\rho_{ c }\left( V _0- V _1\right) g =\frac{1 V _0}{2} g $

$V +\rho_{ c }\left( V _0- V _1\right)=\frac{ V _0}{2}$

[Equlibrium]

$\rho_c\left(V_0-V_1\right)=\frac{V_0}{2}-V $

$\rho_c=\frac{\frac{V_0}{2}-V}{V_0-V_i} $

if $\rho_c<\frac{1}{2} \quad \Rightarrow \quad \frac{\frac{V_0}{2}-V}{V_0-V_i}<\frac{1}{2} $

$\frac{V_0}{2}-V<\frac{V_0}{2}-\frac{V_i}{2} $

$-V<-\frac{V_i}{2} $

$V >\frac{ V _{ i }}{2} \quad \text { so (A) } $

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 "M.C.Q (1 Marks)" from 9.1 , fluid mechanics→9.1 , fluid mechanics — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A cart of mass $M$ is tied by one end of a massless rope of length $10\, m$. The other end of the rope is in the hands of a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $ x = 0$ and the cart at $x = 10\, m$. If the man pulls the cart by the rope, the man and the cart will meet at the point

A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50\,\, Hz$ . The mass of the wire is $30\,\, g$ and its linear density is $4\, \times \, 10^{-2}\,\, kg/m$ . The speed of the transverse wave at the string is ...... $ms^{-1}$

A research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3\,R/2$ where $ R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth’s surface to be $10 \,N$, the pull on the satellite will be ........ $N$.

The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5\, m/s$ at an angle of $120^°$ with the direction of flow of water. The speed of water in the stream is..........$m/s$

Two simple harmonic motions of angular frequency $100$ and $1000\,\,rad\,s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is

The $r.m.s.$ speed of a certain gas is v at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times, will be ...... $K$

A man goes $10\,km$ downstream in $2\,hrs$ and $30\,km$ upstream in $10\,hrs$ . How much time will be take to swim $40\,km$ in still water........$hrs$

Suppose the pressure at the surface of mercury in a barometer tube is P₁ and the pressure at the surface of mercury in the cup is P_2,

P₁ = 0, P₂ = atmospheric pressure.
P₁ = atmospheric pressure P₂ = 0
P₁ = P₂ = atmospheric pressure.
P₁ = P₂ = 0

If the displacement equation of a particle be represented by $y = A\sin PT + B\cos PT$, the particle executes