Understanding of Field

Q. The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

1. 
2. 
3. 
4. 

Q. If W1, W2 and W3 represents the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3.

1. W1 > W2 > W3
2. W1 = W2 = W3
3. W1 < W2 < W3
4. W2 > W1 > W3

Q. The value of $g$ at the surface of earth is $9.8{\text{m/s}}^2$. Then the value of $g^{\prime }$ at a place $480\text{km}$ above the surface of the earth will nearly be (radius of the earth is $\text{6400}\text{km}$)

1. $9.8{\text{m/s}}^2$
   
2. $7.2{\text{m/s}}^2$
   
3. $8.5{\text{m/s}}^2$
   
4. $4.2{\text{m/s}}^2$
   

Q. A particle is taken to a height $R$ above the earth's surface, where $R$ is the radius of earth. The acceleration due to gravity there is

1. $2.45m/s^2$
2. $4.9m/s^2$
3. $9.8m/s^2$
4. $19.6m/s^2$

Q. A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

1. None of these
2. S will run faster than P
3. P will run faster than S
4. They will both run at the same rate as on the earth

Q.

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho }_{1}and{\rho }_2$. The ratio of the accelerations due to gravity at their surface is

1. 

2. 

3. 

4. 

Q. A weight is suspended from the ceiling of a lift by a spring balance. When the lift is stationary the spring balance reads W. If the lift suddenly falls freely under gravity, the reading on the spring balance will be

1. W
2. 2 W
3. 
4. 0

Q. Two simple pendulums of lengths 1 m and 25 m, respectively, are both given small displacement in the same direction at the same instant. If they are in phase after the shorter pendulum has completed n oscillations, then n is equal to

1. $\frac{4}{3}$
2. $\frac{5}{4}$
3. $\frac{7}{5}$
4. $\frac{8}{7}$

Q. If the radius of earth be increased by a factor of $5$, by what factor its density be changed to keep the value of $g$ the same ?

1. $\frac{1}{25}$
2. $\frac{1}{5}$
3. $\frac{1}{\sqrt{5}}$
4. $5$

Q.

A spring has a certain mass suspended from it and its period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

1. 

2. 

3. 2T

4. 

Q. If $W_1,W_2$ and $W_3$ represent the works done in moving a particle from $\text{A}$ to $\text{B}$ along three different paths $\text{1, 2}$ and $\text{3}$ respectively, (as shown in the figure) in the gravitational field of a point mass $m$, find the correct relation between $W_1,W_2$ and $W_3$.

1. $W_1>W_2>W_3$
2. $W_1=W_2=W_3$
3. $W_1<W_2<W_3$
4. $W_2>W_1>W_3$

Q. A schwarzschild black hole is characterized by its mass M and a mathematical spherical surface of radius $R_s=\frac{2GM}{C^2}$ called the event horizon. If the radial distance of an objec r from the black hole is such that $r<R_s,$ then the object is "swallowed " by the black hole and r rapidly decreased to the singular point $r=0.$ Find the minimum energy $E_{min,}$ in $\text{MeV}$, required to dissociate this BHP atom from the ground state.

Q. Two pendulums of length $1.21mand1.0m$ start vibrating. At some instant, the two are in the mean position in same phase. After how many vibrations of the longer pendulum, the two will be in phase ?

1. $10$
2. $11$
3. $20$
4. $21$

Q.

A satellite is orbiting around the Earth at a distance $5times$ the radius of the Earth from its centre. If the acceleration due to gravity on the Earth is $9.8m{s}^{-2}$, calculate the acceleration due to gravity acting of spaceship.

Q. Two springs are connected to a block of mass $M$ placed on a frictionless surface as shown below. If both the springs have a spring constant $k$, the frequency of oscillation of block is

1. $\frac{1}{2\pi }\sqrt{\frac{k}{M}}$
2. $\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$
3. $\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$
4. $\frac{1}{2\pi }\sqrt{\frac{M}{k}}$

Q. The length of a second pendulum at the surface of earth is $1m$. The length of second pendulum at the surface of moon, where $g$ is $\frac{1}{6}th$ that of earth's surface.

1. $\frac{1}{6}m$
2. $\frac{1}{36}m$
3. $6m$
4. $36m$

Q. The mass and diameter of a planet are twice those of earth. The period of oscillation of a pendulum on this planet if it is a seconds pendulum on earth is:

1. 2$\sqrt{3}$s
2. 2$\sqrt{2}$s
3. 2s
4. 4s

Q.

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

1. 

2. 

3. 

4. 

Q. The time period of a simple pendulum on the surface of the earth is $4$s. Its time period on the surface of the moon is:

1. $4$s
2. $8$s
3. $10$s
4. $12$s

Q. A point $P$ is on the axis of a fixed ring of mass $M$ and radius $R$, at a distance $2R$ from the centre $O$. A small particle starts from $P$ and reaches $O$ under the gravitational attraction only. Its speed at $O$ will be

1. zero
2. $\sqrt{\frac{2GM}{R}}$
3. $\sqrt{\frac{2GM}{R}(\sqrt{5}-1})$
4. $\sqrt{\frac{2GM}{R}(1-\frac{1}{\sqrt{5}})}$

Q. If the distance between two particles is reduced to half, the gravitational attraction between them will be

1. Halved
2. Doubled
3. Quadrupled
4. Reduced to a quarter

Q. If W1, W2 and W3 represents the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3.

1. W1 > W2 > W3
2. W1 = W2 = W3
3. W1 < W2 < W3
4. W2 > W1 > W3

Q. A man is standing at a spring platform. Reading of spring balance is $60kg.wt$. If man jumps outside platform, then reading of spring balance:

1. decreases
2. increases
3. first increases then decreases to zero
4. remains same

Q. What is the weight of a 70 kg body on the surface of a planet whose mass is $\frac{1}{7}$ th that of earth and radius is half of earth?

1. 20 kg
2. 40 kg
3. 70 kg
4. 140 kg

Q. The reason for the absence of atmosphere on moon is that the :

1. Value of $v_{rms}$ of the molecules of gas is more that the value of escape velocity
2. Value of $v_{rms}$ of gas is less than escape velocity
3. Value of $v_{rms}$ is negiligible
4. None of above

Q. The ratio of the electrostatic force of attraction to the gravitational force between the proton and electron of the hydrogen atom is of the order of

1. ${10}^{39}$
2. ${10}^{-39}$
3. ${10}^8$
4. ${10}^{-8}$

Q. The mass and radius of a planet are double that of the earth. If the time period of a simple pendulum on the earth is $T$, the time period on the planet is

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

Q. The radii of two planets are respectively $R_1$ and $R_2$ and their densities are $p_1$ and $p_2$. Ratio of the accelerations due to gravity at their surfaces is :

1. $\frac{R_2}{R_1}.\frac{p_1^2}{p_2}$
2. $\frac{R_1}{R_2}.\frac{p_1}{p_2}$
3. $\frac{R_1}{R_2}.\frac{p_2}{p_1}$
4. $1:1$

Q. An object is suspended from a spring balance in a lift. The reading is $240N$ when the lift is at rest. If the spring balance reading now changes to $220N$, the the lift is moving

1. Downward with constant speed
2. Downward with decreasing speed
3. Upward with increasing speed
4. Downward with increasing speed

Q. When a piece of wood is suspended from the hook of a spring balance, it reads $70gf$. The wood is now lowered into the water which results in floating the wood. What reading do you expect on the scale of spring balance?

1. 70gf
2. Zero
3. 35 gf
4. 7gf