Work Done by Force of Gravity

Q.

A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass m will be

1. $\frac{7F}{9}$

2. $\frac{2F}{3}$

3. $\frac{4F}{9}$

4. $\frac{F}{3}$

Q.

Why is there a cos theta in the formula of work done?

Q.

Give an example work done by the force of gravity acting on a body is zero even though the body gets displaced from its initial position.

Q. A simple pendulum of frequency n is taken up to a certain height above the ground and then dropped along with its support so that it falls freely under gravity. The frequency of oscillations of the falling pendulum will

1. Remain equal to n
2. Become greater than n
3. Become less than n
4. Become zero

Q.

A block and tackle system of 5 pulleys is used to raise a load of 50 kgf steadily through a height of 20 m. The work done against friction is 2000J. Calculate the work done by the effort

1. 20000 J

2. 8000 J

3. 16000 J

4. 12000 J

Q.

A boy of mass m climbs up the stairs of vertical height h.

(a) What is the work done by the boy against the force of gravity?

(b) What would have been the work done if he uses a lift in climbing the same vertical height?

Q.

A spherical ball of mass $20kg$ is stationary at the top of a hill of height $100m$. It rolls down a smooth surface to the ground, then climbs up another hill of height of $20m$ above the ground. The velocity attained by the ball is

1. $40m{s}^{-1}$

2. $20m{s}^{-1}$

3. $10m{s}^{-1}$

4. $10\sqrt{30}m{s}^{-1}$

Q.

A body of mass m falls down through a height h. Obtain an expression for the work done by the force of gravity.

Q. A satellite revolves around a planet in a circular orbit. What is the work done by the satellite at any instant? Give a reason.​

Q.

The ratio of SI unit to CGS unit of kinetic energy is

1. 10⁷

2. 10⁵

3. 10^-5

4. 10^-7

Q.

What are the two essential conditions that need to be satisfied for work to be done?

Q.

The frictional force is an example of conservative force.

1. True
2. False

Q.

A block is projected along a rough horizontal road with a velocity of 10 m/s. If the coefficient of kinetic friction is 0.1, how far will it travel before coming to rest?

Q. Masses of 1 kg each are placed 1 m, 2 m, 4 m, 8 m, ...... from a point P. The gravitational field intensity at P due to these masses is

1. 
2. 2G
3. 4G
4. G

Q. Question 3
The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitational force would become

(a) $\frac{F}{4}$
(b) $\frac{F}{2}$
(c) $F$
(d) $2F$

Q.

A particle of mass M is released in vertical plane from a point P at $x$ = $x_0$ on the axis it falls vertically

along the y-axis. Find the torque $\tau$ acting on the particle at a time t about origin?

1. 

2. 

3. 

4. 

Q.

Two blocks identical in shape and size but made of different materials are acted upon equal forces which cause them to slide on a horizontal surface. The acceleration of the second block is found to be 3 times that of the first. What is the ratio of the mass of the second to the first?

1. m₂/m₁ =5/1

2. m₂/m₁ = 1/3

3. m₂/m₁ = 3/1

4. m₁/ m₂ = 2/1

Q.

The average distance between the Sun and Jupiter is 5.2 AU. This distance can also be written as

1. 7.7792 × 10⁸ km

2. 7.7792 × 10⁸ m

3. 6.7652 × 10¹¹ km

4. 6.7652 × 10¹¹ m

Q.

When you lift an object two forces act on it. Which one of the two does positive work.

Q.

Calculate the work done if a particle is moved along a path AB−BC−CD−DE−EF−FA, as shown in the figure in presence of a force $F=\left(\alpha y\hat{i}+2\alpha x\hat{j}\right)N$ , where x and y are in meters and $\alpha =-1N{m}^{-1}$.

Q.

A $2kg$ mass kept on a horizontal table is acted upon by a force of $5N$ at an angle of ${60}^o$ from horizontal and moved through a distance of $3m$ on the table. the work done on the body is

1. $5J$

2. $7.5J$

3. $10J$

4. $15J$

Q.

A body moves in a vertical circle of radius r from the lowest point to highest point. What is the amount of work done by gravitational force during the motion? (Assume mass of the body to be 'm' kg and acceleration due to gravity to be 'g' $\frac{m}{s^2}$)

1. 2mgr

2. mgr

3. 2mg$\pi$r

4. mg$\pi$r

Q.

Give an example where the displacement of a particle is in the direction perpendicular to a force acting on this particle.

Q.

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is [IIT 1985]

1. 

2. 

3. 

4. 

Q.

A person pushes a rock of ${10}^{10}kg$ mass by applying a force of only $10N$ for just $4$ second. The work done is

1. $1000J$

2. zero

3. nearly zero

4. nothing can be decided

Q.

A person lifts a load in the upward direction. He applies force on the load in the upward direction due to which the object is also displaced in the upward direction.

State which of these forces does positive work on the body?

Q. An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure. Find the magnitude of displacement covered by the moving object in $\text{km}$.

1. $13$
2. $11$
3. $9$
4. $7$

Q. Two friends start a race, and together they run for $50\text{m}$. Rohan turns right and runs $60\text{m}$ while Rocky turns left and runs $40\text{m}$. Then Rohan turns left and runs $50\text{m}$ while Rocky turns right and runs $50\text{m}$. How far are the two friends now from each other?

1. $60\text{m}$
2. $20\text{m}$
3. $100\text{m}$
4. $50\text{m}$

Q.

What force should an engine develop, if it causes the displacement of a vehicle through $100m$, such that work done is one mega joule?

Q. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the force constants of the pieces are

1. $\left(\frac{2}{3}\right)k$
2. $\left(\frac{3}{2}\right)k$
3. $3k$
4. $6k$