Question

If the speed of a rod moving at a relativistic speed parallel to its length is doubled,
(a) the length will become half of the original value
(b) the mass will become double of the original value
(c) the length will decrease
(d) the mass will increase

Answer 1

Answer:

(a) is the corrcet answer for the given question

Answer 2

If the speed of a rod moving at a relativistic speed parallel to its length is doubled,(c) the length will decrease  and (d) the mass will increase"

Explanation:

When the rod moves with a particular speed at a relativistic speed v parallel to its length, the mass can be given as

m = $m=m o 1-v 2 c 2$

length = l $=101-\mathrm{v} 2 \mathrm{c} 2=\mathrm{loy}$

where γ = $1+v 22 c 2+\ldots>1 \text { as } v<c$

When there is doubling in the speed, the multiplying factor is denoted as γ’ =$11-4 v 2 c 2=1+2 v 2 c 2+\ldots>2 y$ and $\mathrm{I}=\mathrm{Io} \mathrm{y}^{\prime}<\mathrm{lo} 2 \mathrm{y}$,$\sqrt{x} m=y^{\prime} m o>2 y m o$ .

So, there will be an increase in the length and the mass.