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A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : (g = 10 \(\large m/s^2\) )

(A)

\(\large \sqrt {10}\) rad/s

(B)

\(\large \frac{10}{2\pi}\)rad/s

(C)

10 rad/s

(D)

\(\large 10 \pi\)  rad/s

NEET - Medical UG-2019 Hard

Answer & Solution:

\(\large{In ~vertical~direction,\\\text{frictional force balances the weight of cylinder.}\\f_L\geq mg\\\mu N\geq mg~~~\text{(where N is normal force)} \to (i)\\In~horizontal~direction\\ \\N=Mv^2=Mr\omega^2\to(ii)\\From~eq(i)~and ~eq(ii),\\\omega\geq\sqrt{\Large{g\over r\mu}}\\\omega_{min}=\sqrt{{\Large{g\over r\mu}}}=\sqrt{{\Large{10\over 1 \times0.1}}}=10 ~rad~s^{-1} }\)

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Other Questions of the same topic

Q1:

A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm. The torque required to stop after \(\Large 2\pi\) revolutions is

(A)

\(\large 2 \times 10^{-^6} N m\)

(B)

\(\large 2 \times 10 ^{-3} N m\)

(C)

\(\large 12 \times 10^{-4} N m\)

(D)

\(\large 2 \times 10^6 N m\)

NEET - Medical UG-2019 Medium

Q2:

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (\(k_{t}\)) as well as rotational kinetic energy (\(K_{r}\)) simultaneously. The ratio \(K_{t}:K_{t}+K_{r}\) for the sphere is

(A)

10 : 7

(B)

5 : 7

(C)

7 : 10

(D)

2 : 5

NEET - Medical UG-2018 Medium

Q3:

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

(A)

0.25 rad/s\(\large ^{2}\)

(B)

25 rad/s\(\large ^{2}\)

(C)

5 m/s\(\large ^{2}\)

(D)

25 m/s\(\large ^{2}\)

NEET - Medical UG-2017 Easy

Q4:

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s\(\large ^{-2}\)

(A)

25N

(B)

50N

(C)

78.5 N

(D)

157 N

NEET - Medical UG-2014 Medium

Chemistry Biology

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