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Systems Of Particles And Rotational Motion

Q: Consider the following two statements A and B and identify the correct choice.A) The moment of inertia of a rigid body is independent of its angular velocity.B) The radius of gyration of a rotating metallic disc is dependent on its temperature.

(A) Moment of inertia of the rigid body only dependent on the mass of the body and position of the axis of rotation. It is independent of the angular velocity.(B) \$I =mk^{2}\$\$k=\sqrt{\dfrac{T}{m}} (k=\$radius of gyration)\$I_{dist}=\dfrac{mR^{2}}{2}\$\$k=\dfrac{R}{\sqrt{2}}\$and Radius of the metallic disc is dependent on the temperature, because\$A=A_{0}(1+B\Delta T)\$ (Equation of thermal expansion)\$\pi r^{2}=\pi R_{0}^{2}(1+B\Delta T)\$\$r=R_{0}\sqrt{1+B\Delta T}\$

Q: A particle is moving along a fixed circular orbit with uniform speed. Then the correct statement among the following is:

Let fixed orbit have radius 'R' and uniform velocity of the partial is V.According to Question:Angular momentum \$L=M (\vec V\times \vec R)\$ .......(1) Direction \$=\$ Perpendicular to the plane of motion ...(2)\$(\because\$ V, R is constant so \$L\$ will be constant as well\$)\$.from equation 1,2. L will be constant in magnitude and direction.Option C

Q: Which of the following has the maximum momentum?

Momentum is defined as mass times velocity .Calculating for every option in SI units gives maximum value for option D.

Q: Equal volume of two solution having pH = 2 and pH = 10 are mixed together at 90C. Then pH of resulting solution is : (Take Kw at 90C = \$10^{-12}\$)

Kw at 90C is \$10^{-12}\$Hence, Neutral point is 6So, on adding \$pH = 2 (10^{-2} H^{+})\$ and \$pH = 10 (10^{-2} OH)\$Solution lead to the formation of neutral solution i.e.\$ pH = 6\$

Q: When the velocity of a body is doubled

Momentum is directly proportional to the velocity, hence if velocity is doubled momentum will be doubled.

Q: The centre of gravity depends on the acceleration due to gravity at the given place.

centre of gravity depends on shape of object and its mass distribution.so the answer is B.

Q: Which of the following pairs of physical quantities are not analogous to each other in case of translatory motion and rotational motion,

\$Couple\$ and \$Torque\$ are actually in the same context because both are produced due to the application of force. Moreover both are the faces of same coin.Hence they are not analogous to each other.

Physics
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BITSAT Easy Qs Med Qs Hard Qs

Consider the following two statements A and B and identify the correct choice.
A) The moment of inertia of a rigid body is independent of its angular velocity.
B) The radius of gyration of a rotating metallic disc is dependent on its temperature.

A is true but B is false

A is false but B is true

Both A and B are true

Both A and B are false

Easy

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CG of a triangular lamina is at its _____.

Easy

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A particle is moving along a fixed circular orbit with uniform speed. Then the correct statement among the following is:

Angular momentum of particle is constant only in magnitude but its direction changes from point to point

Angular momentum of particle is constant only in direction but its magnitude changes from point to point

Angular momentum of particle is constant both in magnitude and direction

Angular momentum of particle is not constant both in magnitude and direction

Easy

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Which of the following has the maximum momentum?

A 100 kg vehicles moving at 0.02 ms

^{- 1}

A 4 g weight moving at 10,000 cms

^{- 1}

A 200 g weight moving with kinetic energy of 10

^{- 6} J

A 20 g weight after falling one kilometer.

Easy

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Consider the following two statements A and B and identify the correct choice
A) The torques produced by two forces of couple are opposite to each other
B) The direction of torque is always perpendicular to plane of rotation of body

A is true but B is false

A is false but B is true

Both A and B are true

Both A and B are false

Easy

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Equal volume of two solution having pH = 2 and pH = 10 are mixed together at 90C. Then pH of resulting solution is : (Take Kw at 90C = $1 0^{- 12}$ )

2 + log 2

10 log 2

Easy

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When the velocity of a body is doubled

kinetic energy is doubled

acceleration is doubled.

momentum is doubled.

potential energy is doubled.

Easy

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The centre of gravity depends on the acceleration due to gravity at the given place.

True

False

Easy

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The centre of gravity of regular shaped objects is at their _____.

Easy

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Which of the following pairs of physical quantities are not analogous to each other in case of translatory motion and rotational motion,

force, torque

mass, moment of inertia

couple, torque

linear momentum, angular momentum

Easy

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Systems Of Particles And Rotational Motion

Physics 12691 Views

Consider the following two statements A and B and identify the correct choice. A) The moment of inertia of a rigid body is independent of its angular velocity. B) The radius of gyration of a rotating metallic disc is dependent on its temperature.

CG of a triangular lamina is at its _____.

A particle is moving along a fixed circular orbit with uniform speed. Then the correct statement among the following is:

Which of the following has the maximum momentum?

Consider the following two statements A and B and identify the correct choice A) The torques produced by two forces of couple are opposite to each other B) The direction of torque is always perpendicular to plane of rotation of body

Equal volume of two solution having pH = 2 and pH = 10 are mixed together at 90C. Then pH of resulting solution is : (Take Kw at 90C = 10−12)

When the velocity of a body is doubled

The centre of gravity depends on the acceleration due to gravity at the given place.

The centre of gravity of regular shaped objects is at their _____.

Which of the following pairs of physical quantities are not analogous to each other in case of translatory motion and rotational motion,

Physics
12691 Views

Consider the following two statements A and B and identify the correct choice.
A) The moment of inertia of a rigid body is independent of its angular velocity.
B) The radius of gyration of a rotating metallic disc is dependent on its temperature.

Consider the following two statements A and B and identify the correct choice
A) The torques produced by two forces of couple are opposite to each other
B) The direction of torque is always perpendicular to plane of rotation of body

Equal volume of two solution having pH = 2 and pH = 10 are mixed together at 90C. Then pH of resulting solution is : (Take Kw at 90C = $1 0^{- 12}$ )