A uniform cylinder of mass M and radius R is to be pulled over a step… | JEE Main 2020 (2 Sep, Shift 1)

Q29JEE Main 2020 · 2 SEP · SHIFT 1Difficult

Torque, Couple & Equilibrium of Rigid Bodies

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

Show answer and solution

Answer: (a)

Just before lift-off the floor reaction is zero; take moments about the step edge P (the cylinder pivots about it).
$F$ at O is perpendicular to OP, so its arm is $R$ (the largest possible), which gives the minimum $F$ .
Weight arm = horizontal distance of O from P $= \sqrt{R^2 - (R-a)^2}$
$F R = Mg\sqrt{R^2 - (R-a)^2} \Rightarrow F = Mg\sqrt{1 - \left(\frac{R-a}{R}\right)^2}$
So the answer is (a).

Report a mistake

More questions on Torque, Couple & Equilibrium of Rigid Bodies

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying…JEE Main 2020 (7 Jan, Shift 2)
The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the…JEE Main 2019 (11 Jan, Shift 2)
A rod l m long is acted upon by a couple as shown in the figure. The moment of couple is…MHT CET 2019 (3 May, Shift 1)
The dimensions of torque are same as that ofMHT CET 2019 (2 May, Shift 1)
A slab is subjected to two forces F₁ and F₂ of same magnitude F as shown in the figure…JEE Main 2019 (11 Jan, Shift 1)
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string…JEE Main 2019 (9 Jan, Shift 1)
The moment of the force, F = 4i+5j-6k at (2, 0, –3), about the point (2, –2, –2), is…NEET 2018
A force of 40 N acts on a point B at the end of an L -shaped object, as shown in the…JEE Main 2018 (15 Apr, Shift 1)

Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2020 (2 Sep, Shift 1)

More questions on Torque, Couple & Equilibrium of Rigid Bodies