Answer

Verified

341.1k+ views

**Hint:**We know that frictional force works in a direction opposite to force, so we get

$ F-f=ma $

Now, for rotational motion, torque is required to produce an angular acceleration of an object. Therefore $ $ Torque $ =\text{I}\alpha $

Also,

Torque $ =r\times F $ Here F= linear force

On comparing these equations and substituting the value of I for the cylindrical area, we can find the value of F.

**Complete step by step solution**

We know that Force F=ma

When frictional force is working in direction opposite to F, then equation becomes

F $ - $ f=ma…….. (1) Where f=frictional force

Now, we know that

Torque $ =I\alpha $ …… (2)

Here I=moment of inertia and $ \alpha $ =angular acceleration

Also, Torque=R $ \times $ f…… (3)

Comparing equations (2) and (3), we get

I $ \alpha $ =R f

For a cylindrical roller

I $ =\dfrac{1}{2}m{{R}^{2}} $

Hence,

$ \dfrac{1}{2}m{{R}^{2}}\alpha = $ R f

$ \dfrac{1}{2}mR\alpha = $ f……. (4)

Putting value of equation (4) in equation (1), we get

F $ -\dfrac{1}{2}mR\alpha =ma $ ……. (5)

As the cylinder is rolling without slipping the acceleration of point of contact will be zero.

So,

$ \alpha =\dfrac{a}{R} $

Putting this value in equation (5), we get

F $ -\dfrac{1}{2}mR\alpha =ma $

F= $ ma+\dfrac{1}{2}ma $

$ =\dfrac{3}{2}ma $ .

**Note**

Rolling without slipping is a combination of translational and rotational motion where the point of contact is instantaneously at rest.

When an object experiences pure translational motion, all of its points move with the same velocity as the center of mass, that is, in the same direction and with the same speed.

V(r)=v(center of mass)

The object will also move in a straight line in the absence of net external force.

When the object experiences pure rotational motion about its center of mass, all the points move at right angles to the radius in a plane perpendicular to the axis of rotation with speed proportional to distance from the axis of rotation.

V(r)= r w

Thus points on opposite sides of the axis move in opposite directions, points on the axis do not move at all since r=0

V (center of mass)=0

And points on the outer edge move at maximum speed.

When object experiences rolling motion, the point of the object in contact with surface instantaneously at rest

V (point of contact)=0

So, the center of mass of the object moves with speed v (center of mass) =R w and the point farthest from the point of contact moves with twice the speed v (opposite the point of contact) =2R w.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

The branch of science which deals with nature and natural class 10 physics CBSE

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE