JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Kinematics

WhatsApp Email

A huge circular arc of length 4.4 ly subtends an angle ' 4 s ' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second?
Given :

1 ly = 9.46 \times 1 0^{15} m

1 AU = 1.5 \times 1 0^{11} m

(A) $4.5 \times 1 0^{10} s$ ✓ Correct
(B) $4.1 \times 1 0^{8} s$
(C) $3.5 \times 1 0^{6} s$
(D) $7.2 \times 1 0^{8} s$

Answer: (A)

Solution

The radius of the arc is

R = \frac{ℓ}{θ}

with

ℓ = 4.4 ly = 4.4 \times 9.46 \times 1 0^{15} m

and

θ = 4^{''} = 4 \times \frac{π}{180 \times 3600} = 1.94 \times 1 0^{- 5}

rad, so

R = 2.15 \times 1 0^{21} m

. The path length for four revolutions is

4 \times 2 π R = 5.39 \times 1 0^{22} m

. With speed

v = 8 AU/s = 1.2 \times 1 0^{12} m s^{- 1}

t = \frac{4 \times 2 π R}{v} = \frac{5.39 \times 1 0 ^{22}}{1.2 \times 1 0 ^{12}} \approx 4.5 \times 1 0^{10} s .

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Kinematics →

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Kinematics

Solution

More JEE Main questions on Kinematics