Centripetal Force

Q. A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25\times {10}^6$ $m$ above the surface of earth. If earths radius is $6.4\times {10}^{6}m$ and $g=9.8m{s}^{-2}$, then the orbital speed of the satellite is

1. $6.67km{s}^{-1}$
2. $7.76km{s}^{-1}$
3. $8.56km{s}^{-1}$
4. $9.13km{s}^{-1}$

Q. the capacitance of a spherical condenser whose inner sphere is grounded is 1 microfarad.if the spacing between the two spheres is 1 mm then what is the radius of the outer sphere

Q. Three particles $\text{A, B}$ and $\text{C}$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $\text{A}$ is released, keeping the particles $\text{B}$ and $\text{C}$ fixed, the magnitude of instantaneous acceleration of $\text{A}$ is

1. $\sqrt{5}\frac{Gm}{L^2}$
2. $\sqrt{7}\frac{Gm}{L^2}$
3. $\sqrt{2}\frac{Gm}{L^2}$
4. $\sqrt{3}\frac{Gm}{L^2}$

Q. An artificial satellite is moving in a circular orbit around the earth with a speed equal to $\frac{3}{8}$ times the magnitude of the escape velocity from the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth, then the speed with which it hits the surface of the earth is $\sqrt{\frac{23}{n}}\text{km/s}$. Find $n$. (take g = 10 m/s and $R_e$ = 6400 Km)

Q.

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at ${15}^{\circ }$. What is the radius of the loop?

Q.

Four identical particles of equal masses $1kg$ made to move along the circumference of a circle of radius $1m$ under the action of their own mutual gravitational attraction. The speed of each particle will be

1. $\frac{1}{2}\sqrt{\left(1+2\sqrt{2}\right)G}$

2. $\sqrt{\left(1+2\sqrt{2}\right)G}$

3. $\sqrt{\frac{G}{2}\left(2\sqrt{2}-1\right)}$

4. $\sqrt{\frac{G}{2}\left(1+2\sqrt{2}\right)}$

Q.

The time period of a second's pendulum is 2 sec. The spherical bob which is empty from inside has a mass of 50 gm. This is now replaced by another solid bob of same radius but having different mass of 100 gm. The new time period will be

1. 4 sec

2. 1 sec

3. 2 sec

4. 8 sec

Q. A uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with a force $F$ (see the figure). $F$ is proportional to

1. $\frac{1}{{ϵ}_0}{\sigma }^2{R}^2$
2. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R}$
3. $\frac{1}{{ϵ}_0}{\sigma }^{2}R$
4. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R^2}$

Q.

What is the smallest unit of time?

Q. If the time period of simple pendulum on the surface of earth is T. If the same pendulum is taken at the planet whose mass and radius both are three times as compare to the earth. The time periods of oscillation is –

1. 3T
2. $\frac{1}{\sqrt{3}}$ T
3. $\sqrt{3}$ T
4. $\frac{T}{3}$

Q.

An object weighs $10N$ at the north pole of the earth. In a geostationary satellite distance $7R$ from the centre of the earth (of radius $R$). What are the true weight and the apparent weight?

Q.

a person sitting in the satellite feels weightlessness but a person standing on the moon has weight though the moon is also a satellite of the earth. why?

Q. Mass ${}^{\prime }{m}^{\prime }$ is suspended from the massless pulley which itself is supported by two springs connected to each other as shown. If the mass is slightly displaced from its equilibrium position, the frequency of resulting SHM of mass ${}^{\prime }{m}^{\prime }$ is

1. $\frac{1}{2\pi }\sqrt{\frac{k_1{k}_2}{(k_1+k_2)m}}$
2. $\frac{1}{2\pi }\sqrt{\frac{2k_1{k}_2}{(k_1+k_2)m}}$
3. $\frac{1}{4\pi }\sqrt{\frac{2k_1{k}_2}{(k_1+k_2)m}}$
4. $\frac{1}{\pi }\sqrt{\frac{k_1{k}_2}{(k_1+k_2)m}}$

Q.

Calculate the height from the Earths surface that a satellite must attain in order to be in geosynchronous orbit and the satellites velocity?

Q. A double star system consists of two stars $\text{A}$ and $\text{B}$ which have time periods $T_A$ and $T_B,$ radius $R_A$ and $R_B$ and the mass $M_A$ and $M_B$ respectively. Then

1. If $T_A>T_B^{\prime }$ then $R_A>R_B$
2. If $T_A>T_B^{\prime }$ then $M_A>M_B$
3. ${\left(\frac{T_A}{T_B}\right)}^2={\left(\frac{R_A}{R_B}\right)}^3$
4. $T_A=T_B$

Q. What is the formula of longitudinal magnification with respect to linear magnification?

Q. Suppose a vertical tunnel is dug along the diameter of earth, assumed to be a sphere to be of uniform mass density $\rho$. If a body of mass $m$ is thrown in this tunnel, then its acceleration at a distance $y$ from the centre is given by

1. $\frac{4\pi }{3}G\rho ym$
2. $\frac{1}{4}\pi \rho Gy$
3. $\frac{4}{3}\pi \rho y$
4. $\frac{4}{3}\pi G\rho y$

Q.

How the weight of an object on Earth is six times the weight on the moon?

Q.

Two electrons, each of mass 9.1 x 10^-31 kg, are at a distance 10 Å. Calculate the gravitational force of attraction between them. (G = 6.67 x 10^-11 Nm² kg^-2 ; 1 Å = 10^-10 m)

Q. Three stars, each of mass $m$, are located at the vertices of an equilateral triangle of side $a$. They revolve in circular orbit under mutual gravitational force while preserving the equilateral triangle. Find the mechanical energy of the system.

1. $+\frac{G{m}^2}{2a}$
2. $-\frac{3G{m}^2}{2a}$
3. $-\frac{G{m}^2}{2a}$
4. $+\frac{3G{m}^2}{2a}$

Q.

What is the orbital velocity of the planet?

Q.

If a satellite is orbiting the earth very close to its surface, then the orbital velocity mainly depends on

1. The mass of the satellite only

2. The radius of the earth only

3. The orbital radius only

4. The mass of the earth only

Q.

Where will 2 kg of sugar be profitable to buy? ... at equator or at pole

Q. Consider a hypothetical planet which is very long and cylindrical. The density of the planet is $\rho$ and its radius is $R$. The possible orbital speed of the satellite in moving around the planet in circular orbit in a plane which is perpendicular to the axis of the planet is $\sqrt{x\pi G\rho }R$. The value of $x$ is ________.

Q. A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1$, and that below the piston is $l_2$, such that $l_1>l_2$. Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T$. If the piston is stationary, its mass, $m$ will be given by:
($R$ is the universal constant and $g$ is the acceleration due to gravity)

1. $\frac{RT}{ng}\left[\frac{l_1-3l_2}{l_1{l}_2}\right]$
2. $\frac{RT}{g}\left[\frac{2l_1+l_2}{l_1{l}_2}\right]$
3. $\frac{nRT}{g}\left[\frac{l_1-l_2}{l_1{l}_2}\right]$
4. $\frac{nRT}{g}[\frac{1}{l_2}+\frac{1}{l_1}]$

Q. Two planets have masses $M$ and $16M$ and their radii are $a$ and $2a$, respectively. The separation between the centres of the planets is $10a$. A body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is :

1. $2\sqrt{\frac{GM}{a}}$
2. $4\sqrt{\frac{GM}{a}}$
3. $\sqrt{\frac{G{M}^2}{ma}}$
4. $\frac{3}{2}\sqrt{\frac{5GM}{a}}$

Q.

The weight of a body will be half its weight on the surface of earth when the distance above the surface of the earth is nearly

Q. A body of mass ‘m’ is projected from the surface of a planet (of radius R and mass M) to the surface of another planet (of radius 2R and mass 16M). The distance between the centers of the two spherical planets is 10R. Find minimum speed given to ‘m’ so that it reaches other planet.

Q. What is mediated particles ? Meaning of- gravitational force are not affected by presence of other bodies and intervening medium.

Q. Three identical stars of mass $m$ each are located at the corner of equilateral triangle of side $L$ and are orbiting under mutual gravitational force. Orbital speed of such 3 star system is $V_0=\sqrt{\frac{pGm}{L}}$ then $p$ is