Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
1.5 J
50 J
10 J
100 J
Advertisements
उत्तर
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 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 50 J.
Explanation:
Given, v = ax3/2
m = 0.5 kg, a = 5 m–1/2s–1, work done (W) = ?
We know that
Acceleration `a_0 = (dv)/(dt)` = `v (dv)/(dx) = ax^(3/2) d/(dx) (ax^(3/2))`
= `ax^(3/2) xx a xx 3/2 xx x^(1/2)`
= `3/2 a^2x^2`
Now, Force = `ma_0 = m 3/2 a^2x^2`
Work done = `int_(x = 0)^(x = 2) Fdx`
= `int_0^2 3/2 ma^2x^2dx`
= `3/2 ma^2 xx (x^3/3)_0^2`
= `1/2 ma^2 xx 8`
= `1/2 xx (0.5) xx (25) xx 8`
= 50 J
APPEARS IN
संबंधित प्रश्न
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
`F = -hati+2hatj+3hatkN`
Where `hati,hatj,hatk` are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?
When you hold a pen and write on your notebook, what kind of force is exerted by you on the pen? By the pen on the notebook? By you on the notebook?
Figure shows a boy pulling a wagon on a road. List as many forces as you can which are relevant with this figure. Find the pairs of forces connected by Newton's third law of motion.
Figure shows a cart. Complete the table shown below.
| Force on | Force by | Nature of the Force | Direction |
| Cart |
1 |
||
| Horse |
1 |
||
| Driver |
1 |
Which of the following systems may be adequately described by classical physics ?
(a) motion of a cricket ball
(b) motion of a dust particle
(c) a hydrogen atom
(d) a neutron changing to a proton.
Two spherical bodies, each of mass 50 kg, are placed at a separation of 20 cm. Equal charges are placed on the bodies and it is found that the force of Coulomb repulsion equals the gravitational attraction in magnitude. Find the magnitude of the charge placed on either body.
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.
The magnetic force on a charged particle is always perpendicular to its velocity. Can the magnetic force change the velocity of the particles? Speed of the particle?
The work done by the external forces on a system equals the change in
The work done by all the forces (external and internal) on a system equals the change in ______.
A man moves on a straight horizontal road with a block of mass 2 kg in his hand. If he covers a distance of 40 m with an acceleration of 0⋅5 m/s2, find the work done by the man on the block during the motion.
A block of mass 250 g slides down an incline of inclination 37° with uniform speed. Find the work done against friction as the block slides through 1m.
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.
Find the average frictional force needed to stop a car weighing 500 kg at a distance of 25 m if the initial speed is 72 km/h.
A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in metre. Work done by this force to move the particle from y – 0 to y – 1 m is:
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.
A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.
If a force varies linearly with displacement, the area under the F-s graph forms:
A particle moves under the effect of a force F = Cx from x = 0 to x = x1. The work done in the process is ______.
