A solid sphere rotates about a vertical axis on frictionless bear… - Vidyadip

MCQ

A solid sphere rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of sphere, then passes through over a solid cylinder and then is connected to block of mass $M$ as shown in figure. If the system is released from rest then the speed acquired by block after it has fallen through distance $h$ is

A
$\sqrt {\frac{{10gh}}{9}} $
✓
$\sqrt {\frac{{20gh}}{19}} $
C
$\sqrt {\frac{{15gh}}{139}} $
D
$\sqrt {\frac{{18gh}}{159}} $

✓

Answer

Correct option: B.

$\sqrt {\frac{{20gh}}{19}} $

b
$\mathrm{T}_{1} \mathrm{R}=\frac{2}{5} \mathrm{MR}^{2} \times \frac{\mathrm{a}}{\mathrm{R}}$

$\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right) \mathrm{R}=\frac{1}{2} \mathrm{MR}^{2} \frac{\mathrm{a}}{\mathrm{R}}$

$\mathrm{Mg}-\mathrm{T}_{2}=\mathrm{Ma}$

$\mathrm{Mg}=\mathrm{Ma}\left(\frac{2}{5}+\frac{1}{2}+1\right)$

$g=a \times \frac{19}{10}$

$a=\frac{10 g}{19}$

$v=\sqrt{2 \mathrm{as}}$

$v=\sqrt{2 \times \frac{10 g h}{19}}$

$v=\sqrt{\frac{20 g h}{19}}$

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

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

Similar questions

A spherical planet has a mass $M$ and diameter $D$ . A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity , equal to

In the options given below, let $\mathrm{E}$ denote the rest mass energy of a nucleus and $\mathrm{n}$ a neutron. The correct option is

A man grows into a giant such that his linear dimensions increase by a factor of $9$. Assuming that his density remains same, the stress in the leg will change by a factor of

When the speed of electrons increases, then the value of its specific charge

The distance between the two charges $ + q$ and $ - q$ of a dipole is $r$. On the axial line at a distance $d$ from the centre of dipole, the intensity is proportional to

Which of the following statement is false for the properties of electromagnetic waves ?

In the circuit shown if the $emf$ of source at an instant is $5\, V$, the potential difference across capacitor at the same instant is $4\, V$. The potential difference across $R$ at that instant may be .....$V$

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ with a potential difference $V$ between the plates, is

If $\mathrm{E}$ and $\mathrm{G}$ respectively denote energy and gravitational constant, then $\frac{\mathrm{E}}{\mathrm{G}}$ has the dimensions of :

A uniform sphere of weight $W$ and radius $5\, cm$ is being held by a string as shown in the figure. The tension in the string will be