A solid sphere and a solid cylinder of same mass and radius are r… - Vidyadip

MCQ

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $\left( k _{\text {sph }}: k _{ cyl }\right)$ is $2: \sqrt{ x }$, then value of $x$ is .............

✓
$5$
B
$10$
C
$15$
D
$20$

✓

Answer

Correct option: A.

$5$

a
For solid sphere $\frac{2}{5} mR ^2= mk _{ mph }^2$

$k _{ sph }=\sqrt{\frac{2}{5}} R$

For solid cylinder $\frac{ mR ^2}{2}= mk _{ cyl }^2$

$\Rightarrow k _{ cyl }=\frac{ R }{\sqrt{2}}$

$\frac{ k _{ rph }}{ k _{ cyl }}=\frac{\sqrt{\frac{2}{5}}}{\frac{1}{\sqrt{2}}}=\frac{2}{\sqrt{5}}=\frac{2}{\sqrt{ x }}$

$\therefore x =5$

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

Similar questions

The ratio of total energy of all molecules of one mole $O_2$ to the total energy of all molecules of two moles of $He$ at the same temprature is

Which of the following is not a dimensional constant?

A car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$ . The angular acceleration of the wheel is ........ $rad/s^2$

Which of the following time measuring devices is most precise? Give reason for your answer.

The fundamental frequency of air is 300 Hz in a open air argon pipe. The first overtone of open pipe is whose first overtone of other close argon pipe length of close argon pipe is (v = 336m / s):

The work done by the external forces on a system equals the change in:

A constant current $i$ is maintained in a solenoid. Which of the following quantities will increase if an iron rod is inserted in the soleniod along axis?

A student in the laboratory measures thickness of a wire using screw gauge. The readings are $1.22\,mm , 1.23\,mm , 1.19\,mm$ and $1.20\,mm$. The percentage error is $\frac{ x }{121} \%$. The value of $x$ is ..............

A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops w.r.t. the moving man, will be

A body of mass $m$ accelerates uniformly from rest to a speed $v_0$ in time $t_0$. The work done on the body till any time $t$ is