1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?
A
Left arm is longer than the right arm
B
Both the arms are of same length
C
Left arm is shorter than the right arm
D
Every object that is weighed using this balance appears lighter than its actual weight.

Explanation

From principle of moment we know, the anticlockwise moment is equal to clockwise moment when a system is stable or balance.

$$\therefore\,\,\,$$ load $$ \times $$ load arm = effect $$ \times $$ effect arm

When 5 mg weight is placed on the left pan, load arm shift to left side, hence left arm become shorter than right arm.
2
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :
A
$${{2\,\,mg} \over {2\,m + M}}$$
B
$${{2\,\,Mg} \over {2\,m + M}}$$
C
$${{2\,\,mg} \over {2\,M + m}}$$
D
$${{2\,\,Mg} \over {2\,M + M}}$$

Explanation



From figure, we can say

ma = mg $$-$$ T . . . . . (1)

Moment of inertia of a uniform disc,

I = $${1 \over 2}$$ MR2

and the acceleration of the disc, a = $$ \propto $$ R

We know,

Torque = I$$ \propto $$ = RT

$$\therefore\,\,\,$$ RT = $${1 \over 2}$$ M R2 $$ \times $$ $${a \over R}$$ = $${{MaR} \over 2}$$

$$ \Rightarrow $$ $$\,\,\,$$ T = $${{Ma} \over 2}$$

Putting the value of T in eq (1).

ma = mg $$-$$ $${{Ma} \over 2}$$

$$ \Rightarrow $$ $$\,\,\,$$ a ( m + $${{Ma} \over 2}$$) = mg

$$ \Rightarrow $$ $$\,\,\,$$ a = $${{2mg} \over {2m + M}}$$
3
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

A
Constant speed
B
decreasing speed
C
increasing speed
D
speed which is $${3 \over 4}$$th of that of the roller when the weight is 0.4 m above the ground
4
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

A circular hole of radius $${R \over 4}$$ is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is :

A
$${{219\,M{R^2}} \over {256}}$$
B
$${{237\,M{R^2}} \over {512}}$$
C
$${{19\,M{R^2}} \over {512}}$$
D
$${{197\,M{R^2}} \over {256}}$$

Explanation

Mass of removed disc = $${M \over {16}}$$ Radius of removed disc = $${R \over 4}$$

Moment of inertia of removed disc about it's own axis (O')

= $${1 \over 2}$$ $$ \times $$ $${M \over {16}}$$ $$ \times $$ $${\left( {{R \over 4}} \right)^2}$$ = $${{M{R^2}} \over {512}}$$

Moment of inertia of removed disc about O,

= Icm + mx2

= $${{M{R^2}} \over {512}}$$ + $${M \over {16}}{\left( {{{3R} \over 4}} \right)^2}$$

= $${{19M{R^2}} \over {512}}$$

Moment of inertia of complete disc about point 'O',

I = $${{M{R^2}} \over 2}$$

$$\therefore\,\,\,$$ Moment of Inertia of remaining disc

= $${{M{R^2}} \over 2}$$ $$-$$ $${{19M{R^2}} \over {512}}$$

= $${{237M{R^2}} \over {512}}$$

Questions Asked from Rotational Motion

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