Work Energy Theorem

Q. 18. 1 joule of energy is to be converted into new system of units in which length is measured in 10 metre, mass in 10 kg and time in 1 minute. The numerical value of 1 J in the new system is(1) 36 x 10-4 (2) 36 x 10-2 (3) 36 x 10-3 (4)36×10-

Q.

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

1. 

2. 

3. 

4. 

Q.

A body of mass 5 kg is moving with a momentum of 10 kg-m/s.A force of 0.2 N acts on it in the direction of motion of the body for 10 seconds. The increase in its kinetic energy is

1. 2.8 J

2. 3.2 J

3. 3.8 J

4. 4.4 J

Q.

The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to

1. 

2. Independent of m

3. 

4. m

Q.

A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be

1. 100%

2. 95%

3. 5%

4. 50%

Q.

A particle moving in the $xy$ plane experiences a velocity-dependent force, where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $v$. If $a$ is the acceleration of the particle, then which of the following statements is true for the particle?

1. The kinetic energy of the particle is constant in time.

2. quantity $v\times a$ is constant in time

3. quantity $v.a$ is constant in time

4. $F$ arises due to a magnetic field

Q.

A wire, which passes through the hole in a small bead, is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies to the wire is

1. Always radially outwards

2. Always radially inwards

3. Radially outwards initially and radially inwards later

4. Radially inwards initially and radially outwards later

Q.

A force of 5 N, making an angle $\theta$ with the horizontal, acting on an object displaces it by 0.4 along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force is

1. 1.5 N

2. 2.5 N

3. 3.5 N

4. 4.5 N

Q.

The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 5m, its kinetic energy would be

1. 40 J

2. 50 J

3. 20 J

4. 10 J

Q.

A constant power $P$ is applied to a car starting from rest. If $v$ is the velocity of the car at time $t$, then

1. $v\propto t$

2. $v\propto 1/t$

3. $v\propto \surd t$

4. $v\propto 1/\surd t$

Q.

A constant force F is applied on a body at rest. The power (P) generated is related to the time elapsed (t) as

1. 

2. 

3. 

4. 

Q.

A block of mass m moving with a velocity v hits a light spring of stiffness K attached rigidly to a stationary sledge of mass M. Neglecting friction between all contacting surfaces, the maximum compression of the spring is

1. 

2. 

3. 

4. 

Q.

A body dropped from a height H reaches the ground with a speed of 1.2 $\sqrt{gH}$.Calculate the work doneby air-friction.

1. - 0.28 mgH

2. -0.72 mgH

3. -0.72 mgH

4. 1.2 mgH

Q. A bullet of mass 4 g when fired with a velocity of 50 m/s, can enter a wall up to a depth of 10 cm. How much will be the average resistance offered by the wall?

Q. 35.a bullet of mass 20 g leaves a riffle at an initial speed 100 m/s and strike a target at the same level , with speed 50m/s.the amount of workdone bythe resistance of air will be ?

Q. 1 joule of energy is to be converted into new system of units in which lenght is measured in 10metre, mass in 10kg and time in 1minute. The numerical value of 1 J in the new system is?

Q. A block of mass $m$ is moving with an initial velocity $v_0$ towards a stationary spring of stiffness $k$ attached to the wall as shown. Find the maximum compression in the spring.

1. $v_0\sqrt{\frac{m}{k}}$
2. $v_0\sqrt{\frac{k}{m}}$
3. $2v_0\sqrt{\frac{m}{k}}$
4. $2v_0\sqrt{\frac{k}{m}}$

Q. 49. A particle is executing linear simple harmonic motion of amplitude A. What fraction of the total energy is kinetic when the displacement is half the amplitude 1) 1/4 2) 1/(22) 3) 1/2 4) 3/4

Q.

If the momentum of a body is increased by $100\%$, then the percentage increase in the kinetic energy is

1. $150\%$

2. $200\%$

3. $225\%$

4. $300\%$

Q.

A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earths surface. The height to which it would rise is

1. 

2. 

3. R

4. 2 R

Q. A body of mass $5\text{kg}$ is acted upon by a variable force which varies with the displacement of the body as shown in figure. What is the speed of the body when it has covered $25\text{m}$? (Assume that the body starts from rest.)

1. $100\text{m/s}$
2. $10\text{m/s}$
3. $25\text{m/s}$
4. $20\text{m/s}$

Q. The position $x$ of a particle having mass $m$ moving along $x$ - axis at time $t$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in $\text{m}$ and $t$ in $\text{s}$. Find the work done by the force in first $4\text{s}$.

1. $0\text{J}$
2. $2\text{J}$
3. $4\text{J}$
4. $8\text{J}$

Q.

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = a) is

[MP PMT 1987; CPMT 1990; DPMT 1996;

MH CET 1997, 99; AFMC 1999; CPMT 2000]

1. 

2. 

3. 

4. 

Q. 20. A particle is executing SHM with total mechanicalenergy 90 J and amplitude 6 cm. If its energy issomehow decreased to 40 J then its amplitude willbecome(1) 2 cm(2) 4 cm84(4) cm(3) cm

Q.

The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to t is

1. Directly proportional to t²

2. Independent of t

3. Directly proportional to t

4. Directly proportional to t⁴

Q. A constant force acts on a particle and its displacement x (in cm) is related to the time (in s) by the equationt x+3, when the velocity of the particle is zero, its displacement (in cm) is

Q. A bullet leaving the muzzle of a rifle barrel with a velocity $v$ penetrates a plank and loses ${\frac{1}{5}}^{th}$ of its velocity. It then strikes the second plank, which it just penetrates through. Find out the ratio of the thickness of the planks. [Supposing the average resistance to the penetration is the same in both the case]

1. $\frac{3}{4}$
2. $\frac{9}{16}$
3. $\frac{16}{25}$
4. $\frac{9}{25}$

Q. A block of mass $m$ lying on a smooth horizontal surface is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is

1. $\frac{\pi F}{\sqrt{mk}}$
2. $\frac{F}{\sqrt{mk}}$
3. $\frac{2F}{\sqrt{mk}}$
4. $\frac{F}{\pi \sqrt{mk}}$

Q. A position dependent force $F$ is acting on a particle and its force position curve is shown in the figure. Change in kinetic energy of the particle, when its displacement is from $0$ to $5\text{m}$ is

1. $5\text{J}$
2. $10\text{J}$
3. $15\text{J}$
4. $20\text{J}$

Q.

A block of ice mass 2.0 kg is pushed down an inclined plane of inclination ${37}^{\circ }$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10m/s^2$ If the block started from rest, find the work done$\left(W_f\right)$ by the applied force in the first second, $W_g$ by the weight of the block in the first second and $\left(W_f\right)$ by the frictional force acting on the block in the first second. Take $g=10m/s^2$

1. W_F =100 J; W_g = 100 J; W_f = 0 J

2. W_F =100 J; W_g = 60 J; W_f = 60 J

3. W_F =100 J; W_g = 60 J; W_f = -60 J

4. None of these