A particle moves in a circular orbit of radius ' r ' under a central attractive force, F = -k/r, where k is a constant. The periodic time of its motion is proportional to (a) r1/2 (b) r2/3 (c) r (d) r3/2

Answer: (c). Central force gives the centripetal force: mv²/r = k/r. v = √(k/m), independent of r. T = (2π r)/(v) ∝ r So the answer is (c) r.

A particle moves in a circular orbit of radius ' r ' under a central… | MHT CET 2021 (21 Sep, Shift 1)

Q36MHT CET 2021 · 21 SEP · SHIFT 1Medium

Centripetal Acceleration & Force

A particle moves in a circular orbit of radius ' $r$ ' under a central attractive force, $F = -\frac{k}{r}$ , where $k$ is a constant. The periodic time of its motion is proportional to

Show answer and solution

Answer: (c)

Central force gives the centripetal force: $\frac{mv^2}{r} = \frac{k}{r}$ .
$v = \sqrt{\frac{k}{m}}$ , independent of $r$ .
$T = \frac{2\pi r}{v} \propto r$
So the answer is (c) $r$ .

Report a mistake

More questions on Centripetal Acceleration & Force

A particle is moving with uniform speed along the circumference of a circle of radius R…JEE Main 2021 (26 Feb, Shift 1)
A projectile is thrown with an initial velocity (ai + bj) m/s, where i and j are unit…MHT CET 2021 (23 Sep, Shift 2)
A particle of mass m moves in a circular orbit under the central potential field, U(r) =…JEE Main 2021 (18 Mar, Shift 2)
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration…JEE Main 2020 (6 Sep, Shift 1)
A particle of mass m is performing UCM along a circle of radius r. The relation between…MHT CET 2020 (16 Oct, Shift 2)
A particle of mass m is fixed to one end of a light spring having force constant k and…JEE Main 2020 (8 Jan, Shift 1)
A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm…MHT CET 2019 (2 May, Shift 2)
A body of mass m is performing a UCM in a circle of radius r with speed v. The work done…MHT CET 2019 (3 May, Shift 1)

Centripetal Acceleration & Force question from MHT CET 2021 (21 Sep, Shift 1)

More questions on Centripetal Acceleration & Force