Question

The length of a rod is exactly 1 m when measured at rest. What will be its length when it moves at a speed of (a) 3 × 105 m s−1, (b) 3 × 106 m s−1 and (c) 3 × 107 m s−1?

Answer 1

Explanation:

It is given:

Rod has the proper length, L = 1 m

If v is the rod’s velocity, then the rod has the moving length, which is shown as

$L^{\prime}=L 1-v 2 c 2$

(a) Here,

$v=3 \times 10^{5} \mathrm{m} / \mathrm{s}$

$\mathrm{L}^{\prime}=1 \times 1-9 \times 1016 \times 10109$

=0.9999995 m

(b) Here,

$v=3 \times 10^{6} \mathrm{m} / \mathrm{s}$

$\mathrm{L}^{\prime}=1 \times 1-9 \times 1016 \times 10129=0.99995 \mathrm{m}$

(c) Here,

$v=3 \times 10^{7} \mathrm{m} / \mathrm{s}$

$\mathrm{L}^{\prime}=1 \times 1-9 \times 1016 \times 10149=0.995 \mathrm{m}$