The displacement x of a body of mass 1 kg on smooth horizontal surface as a function of time t is given by x = t 3 3 (where x is in metres and t is in seconds). Find the work done by the external agent for the first second.

Finding the instantaneous velocity and applying work energy theorem holds good here. Work energy theorem states that the work done by all the external forces equals in the change in kinetic energy of the body. x = t 3 3 ⇒ v = d x d t = t 2 The kinetic energy K E = 1 2 m v 2 = 1 2 m t 4 Initial kinetic energy K E i = 0 The final kinetic energy K E f = 1 2 × 1 × 1 2 ⇒ K E f = 1 2 = 0 . 5 J Therefore, the work done by the external agent W = K E f - K E i = 0 . 5 - 0 ⇒ W = 0 . 5 J

The displacement x of a body of mass 1 kg on smooth horizontal surface as a function of time t is given by x = t 3 3 (where x is in metres and t is in seconds). Find the work done by the external agent for the first second.

Finding the instantaneous velocity and applying work energy theorem holds good here. Work energy theorem states that the work done by all the external forces equals in the change in kinetic energy of the body. x = t 3 3 ⇒ v = d x d t = t 2 The kinetic energy K E = 1 2 m v 2 = 1 2 m t 4 Initial kinetic energy K E i = 0 The final kinetic energy K E f = 1 2 × 1 × 1 2 ⇒ K E f = 1 2 = 0 . 5 J Therefore, the work done by the external agent W = K E f - K E i = 0 . 5 - 0 ⇒ W = 0 . 5 J

A particle of mass 10 g is placed in potential field given by V = (50 x 2 + 100) erg/g. What will be frequency of oscillation of particle?

The potential field is given by V = 50 x 2 + 100 erg g - 1 ,The potential energy U = m V = 500 x 2 + 1000 erg The force F = - d U d x = - 1000 x , The restoring force F = - K x ⇒ K = 1000 dyne cm - 1 , Therefore frequency f = 1 2 π K m ⇒ f = 1 2 π 1000 10 ⇒ f = 5 π s - 1

E M B I B E

Beta Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>BEGINNER'S BOX - 2>Q 3

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The displacement $x$ of a body of mass $1 kg$ on smooth horizontal surface as a function of time $t$ is given by $x =$ $\frac{t^{3}}{3}$ (where $x$ is in metres and $t$ is in seconds). Find the work done by the external agent for the first second.

Important Questions on Work, Energy and Power

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Beta Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>BEGINNER'S BOX - 2>Q 4

A bullet of mass

10 g

is moving with speed of

400 m s^{- 1}

. Find its kinetic energy in calories.

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Beta Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>BEGINNER'S BOX - 3>Q 2

The kinetic energy of a particle increases continuously with time. Then, select the correct alternative.

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Beta Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>BEGINNER'S BOX - 3>Q 3

A particle moves in a one-dimensional field with total mechanical energy

E

. If its potential energy is

U (x)

, then

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Beta Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>BEGINNER'S BOX - 3>Q 5

A block weighing $10 N$ travels down a smoothly curved track $A B$ joined to a rough horizontal surface. The rough surface has a friction coefficient of $0.20$ with the block. If the block starts slipping on the track from a point $1.0 m$ above the horizontal surface, then it would move a distance $S$ on the rough surface. Calculate the value of $S$ $[g = 10 m s^{- 2}]$