The Idea of Average Force

Q. Two satellites revolve around the sun, as shown in the figure. The first satellite revolves in a circular orbit of radius $R$ with speed $V_1$. The second satellite revolves in an elliptical orbit, for which minimum and maximum distances from the sun are $R/3$ and $5R/3$ respectively. Velocities of these positions are $V_2$ and $V_3$ respectively. The correct order of speeds is -

1. $V_2>V_1>V_3$
2. $V_2>V_3>V_1$
3. $V_1>V_2>V_3$
4. $V_3>V_1>V_2$

Q. A particle is projected along the inner surface of a smooth vertical circle of radius $R$, its velocity at the lowest point being $\frac{1}{5}\sqrt{95Rg}$. It will leave the circle at angle $\theta$ with the verticle. The angle $\theta$ is

1. ${37}^{\circ }$
   
2. ${53}^{\circ }$
3. ${60}^{\circ }$
4. ${30}^{\circ }$

Q. A frictionless track $\text{ABCDE}$ ends in a circular loop of radius $R$. A body slides down the track from point $\text{A}$ which is at a height $h=5\text{cm}$. Maximum value of $R$ for a body to complete the loop successfully is

1. $2\text{cm}$
2. $\frac{10}{3}\text{cm}$
   
3. $\frac{15}{4}\text{cm}$
4. $\frac{18}{3}\text{cm}$

Q.

A hypothetical spring type object, exerts a force dependent on diplacement x, given by $4x^3$. What is the average force exterted by it while being displaced 2 units from its natural position?

1. 2

2. 4

3. 8

4. 16

Q.

If you performed a work "W" on an object. No external forces are acting on you and the object, while doing this work. Which of the following can be true

1. Work done by the object on you is "-W"

2. Work done on you is "-W"

3. Work done by the object is "-W"

4. Work done by you is "W"

Q. The kinetic energy of a particle moving along a circle of radius $R$ depends on distance $\left(s\right)$ as $K=A{s}^2$ where $A$ is a constant.

The net force acting on the particle is

1. $2As(1+\frac{s}{R})$
2. $As{(1+\frac{s^2}{R^2})}^{1/2}$
3. $2As{(1+\frac{s^2}{R^2})}^{1/2}$
4. zero

Q.

Look at the activity listed here. Reason out whether or not work is done in the light of your understanding of the term work. A green plant is carrying out photosynthesis.

Q.

A hypothetical spring type object, exerts a force dependent on diplacement x, given by $4x^3$. What is the average force exterted by it while being displaced 2 units from its natural position?

1. 2

2. 4

3. 8

4. 16

Q. The kinetic energy of a particle moving along a circle of radius $R$ depends on distance $\left(s\right)$ as $K=A{s}^2$ where $A$ is a constant.

The net force acting on the particle is

1. $2As(1+\frac{s}{R})$
2. $As{(1+\frac{s^2}{R^2})}^{1/2}$
3. $2As{(1+\frac{s^2}{R^2})}^{1/2}$
4. zero

Q. A bead can slide on a smooth circular wire frame of radius $r$ which is fixed in a vertical plane.The bead is displaced slightly from the highest point of the wire frame. The speed of hte bead subsequently as a function of the angle $\theta$ made by the bead with the vertical line is

1. $\sqrt{2gr}$
   
2. $\sqrt{2gr(1-sin\theta )}$
   
3. $\sqrt{2gr(1-cos\theta )}$
   
   
4. $\sqrt{2gr}$
   

Q. What does "work done against the surroundings "mean-- work done on the system or work done by the system?

Q. A particle of mass 1 kg is moving on a circular path of 10 m radius. At any instant of time, its speed is 5 $m{s}^{-1}$ and the speed is increasing at a rate of 2 $m{s}^{-2}$. The net force acting on the particle is

1. $1.2N$
2. $5.2N$
3. $3.2N$
4. $9.2N$

Q.

A freight car is moving on smooth horizontal track without any external force. Rain is falling at the rate of u m/s at an angle $\theta$ with the vertical. Rain drops are collected in the car at the rate of $\mu$ kg/s. If initial mass of the car is $m_0$ and velocity $v_0$ then find its velocity after time it.

1. $v=2ucos\theta (\frac{m_0}{m_0+\mu t}-1)+\frac{m_0{v}_0}{(m_0+\mu t)}$

2. $v=usin\theta (\frac{m_0}{m_0+\mu t}-1)+\frac{3m_0{v}_0}{(m_0+\mu t)}$

3. $v=usin\theta (\frac{m_0}{m_0+\mu t}-1)+\frac{m_0{v}_0}{(m_0+\mu t)}$

4. $Zero$

Q.

A man rows a boat upstream but is at rest with respect to the shore. Is he doing any work?

Q. Two blocks are placed on a smooth horizontal surface and connected by a string pulley arrangement as shown. If a force $F$ starts acting on block $m_1$, then find the relation between acceleration of both masses and their values.

Q.

1. Define energy.
2. State the mathematical expression of work.
3. State two examples of when a force acting on a body does not do any work.

Q. State the factors on which work done depends.

Q.

Read the given statement carefully and answer whether work is done or not done, and why?

A man pushing a wall.