Advertisements
Advertisements
Question
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement-time curve for its motion?
Options
Advertisements
Solution
Explanation:
For constant power
Displacement ∝ t3/2
Because P = `(vecF * dvecs)/(dt) = vecF * vecv` = constant .....(∵ P = constant according to the problem)
Now, will by dimensional analysis
[F][v] = constant
⇒ [MLT–2][LT–1] = constant
⇒ L2T–3 = constant .....(∵ mass is constant)
⇒ L ∝ T3/2
⇒ Displacement (d) ∝ t3/2
APPEARS IN
RELATED QUESTIONS
A body of mass m is placed on a table. The earth is pulling the body with a force mg. Taking this force to be the action what is the reaction?
A lawyer alleges in court that the police had forced his client to issue a statement of confession. What kind of force is this ?
List all the forces acting on the block B in figure.
Mark the correct statements :
(a) The nuclear force between two protons is always greater than the electromagnetic force between them.
(b) The electromagnetic force between two protons is always greater than the gravitational force between them.
(c) The gravitational force between two protons may be greater than the nuclear force between them.
(d) Electromagnetic force between two protons may be greater than the nuclear force acting between them.
Calculate the force with which you attract the earth.
A body builder exerts a force of 150 N against a bullworker and compresses it by 20 cm. Calculate the spring constant of the spring in the bullworker.
Find the ratio of the magnitude of the electric force to the gravitational force acting between two protons.
In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
(a) work by the winning team on the losing team
(b) work by the losing team on the winning team
(c) work by the ground on the winning team
(d) work by the ground on the losing team
(e) total external work on the two teams.
A block of mass m is kept over another block of mass M and the system rests on a horizontal surface (In the following figure). A constant horizontal force F acting on the lower block produces an acceleration \[\frac{F}{2 \left( m + M \right)}\] in the system, and the two blocks always move together. (a) Find the coefficient of kinetic friction between the bigger block and the horizontal surface. (b) Find the frictional force acting on the smaller block. (c) Find the work done by the force of friction on the smaller block by the bigger block during a displacement d of the system.
A block of weight 100 N is slowly moved up a smooth incline of inclination 37° by a person. Calculate the work done by the person in moving the block through a distance of 2 m, if the driving force is (a) parallel to the incline and (b) in the horizontal direction.
A particle of mass m moves on a straight line with its velocity varying with the distance travelled, according to the equation \[\nu = a\sqrt{x}\] , where a is a constant. Find the total work done by all the forces during a displacement from \[x = 0 \text{ to } x - d\] .
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Show that the work done by the applied force does not exceed 40 J.
A 250 g block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of 40 cm/s. If the friction coefficient between the table and the block is 0⋅1, how far does the block move before coming to rest?
Water falling from a 50-m high fall is to be used for generating electric energy. If \[1 \cdot 8 \times {10}^5 \text{ kg } \] of water falls per hour and half the gravitational potential energy can be converted into electrical energy, how many 100 W lamps can be lit with the generated energy?
The work done by an applied variable force, F = x + x3 from x = 0 m to x = 2m, where x is displacement, is:
A body of mass 0.5 kg travels in a straight line with velocity v = a x3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is ______.
A body is being raised to a height h from the surface of earth. What is the sign of work done by applied force?
A graph of potential energy V(x) verses x is shown in figure. A particle of energy E0 is executing motion in it. Draw graph of velocity and kinetic energy versus x for one complete cycle AFA.
If a force varies linearly with displacement, the area under the F-s graph forms:
