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Matter In Our Surroundings

Question
CBSEENSC9006339
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Show that the kinetic energy of a body of mass m moving with velocity v is given bystraight E subscript straight k space equals space 1 half mv squared.

 

Solution

Expression for kinetic energy:
The kinetic energy of a body can be determined by calculating the amount of work required to set the body into motion with the velocity v from its state of rest.

U s i n g space t h e space 3 to the power of r d end exponent space e q u a t i o n space o f space m o t i o n comma space space space space space space space space straight v squared space minus space straight u squared space equals space 2 a s therefore space space space straight v squared space minus space 0 squared space equals space 2 a s space rightwards double arrow space straight a space equals space fraction numerator straight v squared over denominator 2 straight s end fraction
Let m be the mass of the body,
u is the initial velocity of the body,
F = force applied on the body,
a = acceleration produced in the body in the direction of force,
v = final velocity of the body, and
s = distance covered by the body
Now, work done is given by, considering that force and displacement are in the same direction.

 

straight W space equals space Fs space From space Newton apostrophe straight s space first space law space of space motion comma space straight F space equals space ma That space is comma space straight W space equals space ma. space space straight s space space space space space space equals space straight m. space space fraction numerator straight v squared over denominator 2 straight s end fraction cross times space straight s space space space space space space equals space 1 half mv squared
This work done appears as the kinetic energy of the body, given by
therefore space space space straight E subscript straight k space equals space 1 half mv squared., is the kinetic energy of the body. 

 

Some More Questions From Matter In Our Surroundings Chapter

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a) 25°C
b)00C
c)1000C

What is the physical state of water at
0°C

What is the physical state of water at
100°C

Give two reasons to justify
Water at room temperature is a liquid.

Give two reasons to justify
An iron almirah is a solid at room temperature.

Why is ice at 273K more effective in cooling than water at the same temperature ?

What produces more severe burns, boiling water or steam ?

8. Name A, B, C, D, E and F in the following diagram showing state change :

Both boiling and evaporation convert a liquid into vapour. What is the difference between the two process

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