Home
Class 11
PHYSICS
A spring which is initially in un-streat...

A spring which is initially in un-streatched condition, is first stretched by a length x and again by a further length x. The work done in the first case `W_(1)` is one third of the work done in second case `W_(2)`. True of false ?

Text Solution

Verified by Experts

True.
Work done in case - I
`W_(1)=(1)/(2)kx^(2)`
Work done in case - II
`W_(2)=P.E_("final")-P.E_("initial")`
`=(1)/(2)k(2x)^(2)-(1)/(2)kx^(2)`
`=(1)/(2)k(4x^(2)-x^(2))=3((1)/(2)kx^(2))`
`therefore W_(2)=3W_(1)`
`therefore W_(1)=(W_(2))/(3)`
Therefore true.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WORK, ENERGY AND POWER

    PREMIERS PUBLISHERS|Exercise MULTIPLE CHOICE QUESTIONS (OTHER IMPORTANT QUESTIONS & ANSWERS)|124 Videos
  • WORK, ENERGY AND POWER

    PREMIERS PUBLISHERS|Exercise VERY SHORT ANSWER QUESTIONS|34 Videos
  • WORK, ENERGY AND POWER

    PREMIERS PUBLISHERS|Exercise NUMERICAL PROBLEMS|76 Videos
  • WAVES

    PREMIERS PUBLISHERS|Exercise OTHER IMPORTANT & QUESTIONS ANSWERS ( NUMERICAL PROBLEMS. )|48 Videos

Similar Questions

Explore conceptually related problems

A spring which in initially in un-stretched condition, is first stretched by a length x and again by a further length x. The work done in the first case W_(1) is one third of the work done in second case W_(2) . True or false?

A spring which in initially in unstretched condition, is first stretched by a length and again by a further length x. The work done in the first case W_(1) , is one thing of the work done in second case W_(2) . True or false?

Two similar springs p and Q have spring constants Kp and kQ, such that Kp>KQ. The are stretched, first by the same amount ( case a), then by the same force (case b). The work done by the springs Wp and WQ are related as, in case (a) and case (b), respectively:

A wire of length L and cross section A is made of material of young's modulus y. It is stretched by an amount x. What is the work done ?

A body of mass 0.3 kg is taken up an inclined plane to length 10 m and height 5 m and then allowed to slide down to the bottom again. The coefficient of friction between the body and the plane is 0.15. What is the (i) work done by the gravitational force over the round trip? (ii) work done by the applied force over the upward joumey? (iii) work done by frictional force over the round trip? (iv) kinetic energy of the body at the end of the trip? How is the answer to (iv) related to the first three answers?

2.00 mole of a monatomic ideal gas (U=1.5nRT) is enclosed in an adiabatic, fixed , vertical cylinder fitted with a smooth, light adiabatic piston. The piston is connected to a vertical spring of spring constant 200 N m^(-1) as shown in .the area of cross section of the cylinder is 20.0 cm^(2) . initially, the spring is at its natural length and the temperature of the gas is 300K at its natural length. the atmosphere pressure is 100 kPa. the gas is heated slowly for some time by means of an electric heater so as to move the position up through 10 cm. find (a) the work done by the gas (b) the final temperature of the gas and (c ) the heat supplied by the heater.

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring one each mass is

From an equilibrium state A to another equilibrium state A to another equilibrium state B an amount of work equal to 30 J is done on the system .if the gas is taken from state A to B iva a process in which the net heat observe by system is 10 cal , how much is the net work done by the system in the later case. [ Take 1 cal = 4.2 J]

A rod of length 2 units whose one end is (1,0,-1) and other end touches the plane x-2y=2Z+4=0, then a. the rod sweeps the figure whose volume is b .pic . d. cubic units. e. the area of the region which the rod traces on the plane is f . g.2pih . i. j. the length of projection of the rod on the plane is k . l.sqrt(m .3n .)o.p . q. units. r. the centre of the region which the rod traces on the plane is s . t.(u . v. w.2/x .3y . z. , aa.2/b b .3c c . dd. ,-e e .5/f f .3g g . hh. ii.)dotj j . kk.

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is