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 minimum work required to pull the hanging part of the chain on the table is

A particle moves with the velocity $\overrightarrow{\mathrm{v}}=(5\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}}){\mathrm{ms}}^{-1}$ under the influence of a constant force, $\overrightarrow{\mathrm{F}}(2\hat{\mathrm{i}}+5\hat{\mathrm{j}}-10\hat{\mathrm{k}})$ N. The instantaneous power applied is

A body is projected from ground obliquely. During downward motion, power delivered by gravity to it

A body of mass m accelerates uniformly from rest to velocity v₁ in time interval T₁. The instantaneous power delivered to the body as a function of time t is

The power of a pump, which can pump 500 kg of water to height 100 m in 10 s is

Positively charged particles X and Y are initially far away from each other and at rest. X begins to move towards Y with some initial velocity. The total momentum and energy of the system are p and E respectively. Which of the following statement is correct?

A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remains constant during the fall?

Q.11 A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shown the displacement-time curve for its motion?

Q.12 Which of the diagrams shown in the figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?

Q. 13 Which of the diagrams shown in the figure represents the variation of to mechanical energy of a pendulum oscillating in the air as a function of time.

Q. 14 A mass of 5 kg is moving along a circular path of radius 1 m. If the mas moves with 300 rev/min, its kinetic energy would be

Q. 19 A man of mass m, standing at the bottom of the staircase, of height L, climbs it and stands at its top.

(a) Work done by all forces on man is equal to the rise in energy mgL
(b) Work done by all forces on man is zero
(c) Work done by the gravitational force on man is mgL
(d) The reaction force from a step does not do work the point of the application of the force does not move while the force exists

Q. 20 A bullet of mass m fired at 300 to the horizontal leaves the barrel of the gun with a velocity v. The bullet hits a soft target at a height h above the ground while it is moving downward and emerge out with half the kinetic energy it had before hitting the target.

Which of the following statements are correct in respect of the bullet after it emerges out of the target?

(a) The velocity of the bullet will be reduced to half its initial value
(b) The velocity of the bullet will be more than half of its earlier velocity
(c) The bullet will continue to move along the same parabolic path
(d) The bullet will move in a different parabolic path
(e) The bullet will fall vertically downward after hitting the target
(f) The internal energy of the particles of the target will increase

Q.1 An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is, because

(a) the two magnetic forces are equal and opposite, so they produce no net effect

(b) the magnetic forces do not work on each particle

(c) the magnetic forces do equal and opposite (but non-zero) work on each panicle

(d) the magnetic forces are necessarily negligible

Q.2 A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. At the same time t, the work done on the two moving charged particles is

(a) same as the same force law is involved in the two experiments

(b) less for the case of a position, as the position moves away more rapidly and the force on it weakens

(c) more for the case of a position, as the position moves away from a larger distance

(d) same as the work done by cha particle on the stationary proton

Q. 3 A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is

(a) constant and equal to mg in magnitude

(b) constant and greater than mg in magnitude

(c) variable but always greater than mg

(d) at first, greater than mg and later becomes equal to mg

A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200N is directly opposed to the motion. The work done by the cycle on the road is:

Q. 5 A body is falling freely under the action of gravity alone in a vacuum.
Which of the following quantities remain constant during the fall?

(a) Kinetic energy                    (b) Potential energy
(c) Total mechanical energy      (d) Total linear momentum

Q. 7 Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

(a) Both the stones reach the bottom at the same time but not at the same speed

(b) Both the stones reach the bottom with the same speed and the stone reaches the bottom earlier than stone

(c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I

(d) Both the stones reach the bottom at different times and at different speeds

Q.8 The potential energy function for a particle executing linear SHM is given by $\mathrm{V}\left(\mathrm{x}\right)=\frac{1}{2}{\mathrm{kx}}^2$ where k is the force constant of the oscillator (Fig). For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches $\mathrm{x}=\pm {\mathrm{x}}_{\mathrm{m}}$. If V and K indicate the PE and KE, respectively of the particle at $\mathrm{x}=+{\mathrm{x}}_{\mathrm{m}}$, then which of the following is correct?

$\begin{array}{ll}\text{ (a) }\mathrm{V}=\mathrm{O},& \mathrm{K}=\mathrm{E}\\ \text{ (b) }\mathrm{V}=\mathrm{E},& \mathrm{K}=\mathrm{O}\\ \text{ (c) }\mathrm{V}<\mathrm{E},& \mathrm{K}=\mathrm{O}\\ \text{ (d) }\mathrm{V}=\mathrm{O},& \mathrm{K}<\mathrm{E}\end{array}$

A body of mass 0.5 kg travels in a straight line with velocity $\mathrm{v}={\mathrm{ax}}^{3/2}$where $\mathrm{a}=5{\mathrm{m}}^{-1/2}{\mathrm{s}}^{-1}$. The work done by the net force during its displacement from x = 0 m to x = 2 m is-

(a) 15 J                            (b) 50 J

(c) 10 J                            (d) 100 J

If a force $\overrightarrow{\mathrm{F}}=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$ unit acts on a box and the displacement of the box is$\overrightarrow{\mathrm{d}}=\left(5\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)$ unit, the angle between force and displacement is:

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass 1.00 g falling from a height of 1.00 km. It hits the ground with a speed of 50.0 m/s. Work done by the gravitational force and work done by the unknown resistive force respectively are:

A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 200 N and is directly opposed to the motion. Work done by the road on the cycle and work done by the cycle on the road respectively are:

In a ballistics demonstration, a police officer fires a bullet of mass 50.0 g with speed 200 m/s  on soft plywood of thickness 2.00 cm. The bullet emerges with only 10% of its initial kinetic energy. The emergent speed of the bullet is:

A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of 100 N over a distance of 10 m. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to 50 N. The total distance through which the trunk has been moved is 20 m. Plot of force applied by the woman and the frictional force, which is 50 N versus displacement is given below. Work done by the two forces over 20 m are:

A block of mass m = 1 kg, moving on a horizontal surface with speed ${\mathrm{v}}_{\mathrm{i}}$ = 2 m/s enters a rough patch ranging from x = 0.10 m to x = 2.01 m. The retarding force ${\mathrm{F}}_{\mathrm{r}}$ on the block in this range is inversely proportional to x over this range,

${\mathrm{F}}_{\mathrm{r}} = \frac{-\mathrm{k}}{\mathrm{x}}$ for 0.1 < x < 2.01 m

     = 0     for x < 0.1m and x > 2.01 m

where k = 0.5 J. What is the final kinetic energy and speed ${\mathrm{v}}_{\mathrm{f}}$ of the block as it crosses this patch?

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_0$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the horizontal velocity ${\mathrm{v}}_0$ is:

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_0$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the ratio of the kinetic energies ${\mathrm{K}}_{\mathrm{B}}/{\mathrm{K}}_{\mathrm{C}}$ at points B and C is:

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_0$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point. If the connecting string is cut at point C, the trajectory of bob is: