# A string is wound around a hollow cylinder of mass $5kg$ and radius $0.5m$ . If the string is now pulled with a horizontal force of $40N$ , and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be?(Neglect the mass and thickness of the string).

A) \[12rad{s^{ - 2}}\]

B) \[16rad{s^{ - 2}}\]

C) $10rad{s^{ - 2}}$

D) \[20rad{s^{ - 2}}\]

Answer

Verified

288.3k+ views

**Hint:**Since, the force of $40N$ is acting on the cylinder in the right direction (as shown in diagram), then there must be some linear acceleration of the center of mass of the cylinder in the right direction because of the force acting on it. And this force is applied on the edge of the cylinder, then this will generate a torque in the cylinder and due to this torque, the cylinder will roll and hence will have some angular acceleration too.

**Complete step by step answer:**

Let linear acceleration in the direction of net force be a, angular acceleration be $\alpha $ .

Mass of cylinder is $m = 5kg$

Since, the force of $40N$ and force f is acting in same direction, so, equation for linear acceleration will be:

$40 + f = ma$

Replace $a = R\alpha $

$40 + f = mR\alpha $ -----(1)

Now, equation of torque –

$

40 \times R - f \times R = m{R^2}\alpha \\

40 - f = mR\alpha \\

$

Let this be equation 2

Adding equation 2 with equation 1 and putting all given values, we get,

$80 = 2mR\alpha = 2 \times 5 \times 0.5 \times \alpha $

On solving this, we get angular acceleration as,

$\alpha = \dfrac{{80}}{5} = 16rad{s^{ - 2}}$

Hence angular acceleration of the cylinder will be \[16rad{s^{ - 2}}\] .

So correct option is (B)

**Note:**We got equation 2 using relation between torque and force and using force balance. According to the given diagram, torque will be acting in clockwise direction and equation 1 we got using simple linear force balance in the right direction. So the cylinder will be rotating in clockwise direction as well as moving forward in the right direction simultaneously.

Last updated date: 24th May 2023

•

Total views: 288.3k

•

Views today: 4.46k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main