Download App

6. system of particles and rotational motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x}}$. The value of $x$ is $.......$
  • A
    $4$
  • B
    $3$
  • ✓
    $5$
  • D
    $2$
✓

Answer

Correct option: C.
$5$
c
For ring $I=m R_1^2=m K_1^2$

$\therefore$ Radius of gyration $K_1=R_1$

For solid sphere

$I^{\prime}=\frac{2}{5} m^{\prime} R_2^2=m^{\prime} K_2^2$

$\therefore \text { Its radius of gyration }=K_2=\sqrt{\frac{2}{5}} R_2$

$\because K_1=K_2$

$\therefore R_1=\sqrt{\frac{2}{5}} R_2$

$\therefore \frac{R_1}{R_2}=\sqrt{\frac{2}{5}}$

$\therefore x=5$

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 6. system of particles and rotational motion→6. system of particles and rotational motion — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The potential energy of a particle of mass $5kg$ moving in the $XY$ plane is given by $V= -7x+24y$ joules, $x$ and $y$ being in metres. Initially at $t=0$ the particle is at the origin $(0,0)$ moving with $a$ velocity of $6[ \hat i (2.4)+ \hat j (0.7)] m/s$. Then
→
One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight ${W_1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at a height $3L/4$ from its lower end is
→
A block $C$ of mass $m$ is moving with velocity $v_0$ and collides elastically with block $A$ of mass $m$ which connected to another block $B$ of mass $2\,m$ through a spring of spring constant $k$. What is $k$ if $x_0$ is the compression of spring when velocity of $A$ and $B$ is same?
→
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........$hrs$
→
A thin circular ring first slips down a smooth incline then rolls down a rough incline of identical geometry from same height. Ratio of time taken in the two motion is ........
→
A space craft of mass $'M' $ and moving with velocity $ 'v' $ suddenly breaks in two pieces of same mass $m$. After the explosion one of the mass $ 'm'$  becomes stationary. What is the velocity of the other part of craft
→
A thermally insulated container is divided into two parts by a screen. In one part the pressure and temperature are $P$ and $T$ for an ideal gas filled. In the second part it is vacuum. If now a small hole is created in the screen, then the temperature of the gas will
→
A block of mass $m$ is at rest with respect to a lift when placed on inclined plane of  inclination $\theta$ inside the lift. If lift move upward at constant  velocity $v$ then work  done by friction force on block in $t$ time is :-
→
A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11$ $km/s$, the escape velocity from the surface of the planet would be ........  $kms^{-1}$.
→
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32\ V$, the efficiency of the engine is
→