Question

16. (a) The density of an object on the earth is p. What density would be found by an
observer
on the earth if the object is moving at a relative speed of v? (b) The density of lead
on the earth is 1.1x10° kg/m". What density would be found if lead object is moving
at 0.8 c? [2marks]​

Answer 1

Answer:

Write the order in which the density decreases in three states of matter

Explanation:

Answer 2

Given:

the density of object = p

the relative speed of the object = v

Find:

density found by the observer of moving object =?

Solution:

Now let us assume that

mass of object at rest on earth = m1

volume of object at rest on earth = V1

length of object at rest on earth = L1

now given

the density of object at rest on earth = p

Also, density = mass/volume

p = m1/v1

through dimensional analysis we know that the volume is proportional to length cube

v1 ∝ L1³

v1 = kL1³

through this we infer that

$p =\dfrac{m1}{kL1^{3} }$      --------(1)

now through theory of relativity we know that,

change in mass (m2) = $\dfrac{m1}{\sqrt{1-\dfrac{u^{2} }{c^{2} } } }$

let's assume $\dfrac{1}{\sqrt{1-\dfrac{u^{2} }{c^{2} } } }$ be x

then m2 = m1x

similarly, through the theory of relativity, the change in Volume is

$V2 = k\dfrac{L1^{3} }{x^{3} }$

putting these values in equation

for new density p2 = m2/v2

on putting the above values we get

the density would be

$p2 = \dfrac{p}{\ [1-\dfrac{u^{2} }{c^{2} }]^{2} } }$