Three particles of equal mass m are situated at the vertices of a… - Vidyadip

MCQ

Three particles of equal mass $m$ are situated at the vertices of an equilateral triangle of side $l$. They are moving in a circle in influence of their mutual gravitational interaction. Then their time period of revolution is directly proportional to

A
$l^{1/2}$
B
$l^{-1/2}$
✓
$l^{3/2}$
D
$l^{-3/2}$

✓

Answer

Correct option: C.

$l^{3/2}$

c
$\frac{m V^{2}}{\frac{\ell}{\sqrt{3}}}=\frac{\sqrt{3} G m^{2}}{\ell^{2}}$

$V=\sqrt{\frac{G m}{\ell}}$

$\mathrm{T}=\frac{2 \pi \mathrm{r}}{\mathrm{V}}=\frac{2 \pi \times \frac{\ell}{\sqrt{3}}}{\sqrt{\frac{\mathrm{Gm}}{\ell}}}$

T $\propto \ell^{3 / 2}$

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 7. gravitation→7. gravitation — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A particle of mass $5 × 10^{-5}\ kg$ is placed at lowest point of smooth parabola $x^2 = 40y$ ( $x$ and $y$ in $m$ ). If it is displaced slightly such that it is constrained to move along parabola, angular frequency of oscillation (in $rad/s$) will be approximately:-

Two masses $m_1$ and $m_2$ are connected by a string of length $l$. They are held in a horizontal plane at a height $H$ above two heavy plates $A$ and $B$ made of different material placed on the floor. Initially distance between two masses is $a < l$. When the masses are released under gravity they make collision with $A$ and $B$ with coefficient of restitution $0.8$ and $0.4$ respectively. The time after the collision when the string becomes tight is :- (Assume $H>>l$)

A material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be percentage increase in volume is .......... $\%$

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given by

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Suppose the particle when reaches the horizontal surfaces, its velocity with respect to ground is $v_1$ and that of wedge is $v_2$. Choose the correct statement(s)

In a mechanical refrigerator, the low temperature coils are at a temperature of $-23°C$ and the compressed gas in the condenser has a temperature of $27°C.$ The theoretical coefficient of performance is

In which process, the rate of transfer of heat is maximum

Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is:

A circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

A block of mass $4\, kg$ rests on an inclined plane. The inclination of the plane is gradually increased. it is found that when the inclination is $3$ in $5\left( {\sin \theta = \frac{3}{5}} \right)$, the block just begins to slide down the plane. The coefficient of friction between the block and the plane is