Download App

STD 11 - 9.1 , fluid mechanics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9.1 , fluid mechanics4 Marks
MCQ
A solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of cavity radius to that of outer radius of sphere is
  • A
    $\frac{{{{\left( {28} \right)}^{1/3}}}}{3}$
  • B
    $\frac{{{{\left( {30} \right)}^{1/3}}}}{3}$
  • ✓
    $\frac{{{{\left( {26} \right)}^{1/3}}}}{3}$
  • D
    $\frac{{{{\left( {24} \right)}^{1/3}}}}{3}$
✓

Answer

Correct option: C.
$\frac{{{{\left( {26} \right)}^{1/3}}}}{3}$
c
From law of flotation

$\frac{4}{3} \pi \mathrm{R}^{3} \times 1 \times \mathrm{g}=\frac{4}{3} \pi\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \rho \mathrm{g}$

$\mathrm{R}^{3}=\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \times 27$

$\frac{r^{3}}{R^{3}}=\frac{26}{27} \Rightarrow \frac{r}{R}=\frac{(26)^{1 / 3}}{3}$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Match List-I with List-II :- 
 List-I
EM-Wave		 List-II
Wavelength
Range
(A)Infra-red(I)< 10^(-3)nm
(B)Ultraviolet(II)400 nm to 1 nm
(C)X-rays(III)1 mm to 700 nm
(D)Gamma rays(IV)1 nm to 10^(-3)nm
Choose the correct answer from the options given below : 
→
Which of the following physical quantities do not have same dimensions?
→
Four particles each of mass $m$ are placed at the corners of a square of side length $l.$  The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is   
→
An electron changes its position from orbit $n = 4$ to the orbit $n = 2$ of an atom. The wavelength of the emitted radiation’s is ($R =$ Rydberg’s constant)
→
The bulk modulus of rubber is $9.1 \times 10^8\,N/m^2$. To what depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$ ? ....... $m$
→
In the given figure, $a = 15 \,m s^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5\, m$ at a given instant of  time. The speed of the particle is ........ $m/s$
→
Which of the following will have highest penetrating power
→
Figure shows, the adiabatic curve on a $\log T$ and log $V$ scale performed on ideal gas. The gas is ............
→
For an object projected from ground with speed $u$ horizontal range is two times the maximum height attained by it. The horizontal range of object is ..........
→
The resolving power of an astronomical telescope is $0.2\, sec$. If the central half portion of the objective lens is covered, the resolving power will be....$sec$
→