Q: If the resultant of all external forces is zero, then velocity of centre of mass will be

\$F_{external}= M a_{CM}\$ where M is the total mass.Zero net external force implies that \$a_{CM}= 0\$Thus \$V_{CM} = constant\$ OR zero(If the system is at rest initially, then \$V_{CM}= 0\$)

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.

Question 1

CG of a triangular lamina is at its _____.

Accepted Answer

Centroid

Question 2

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

Accepted Answer

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

Question 3

The centre of a mass of a rigid body lies

Accepted Answer

Centre of mass of rigid bodies may lie either inside or outside the body.For example:  COM of solid sphere lies inside it whereas COM of uniform circular ring lies at its geometric centre where there is actually no matter.

Question 4

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

Accepted Answer

The direction of torque is always perpendicular to plane of rotation of body as a cross product is in perpendicular plane to $r$ and $F$ vectors and the torques produced by two forces of couple are in same direction to each other.

Question 5

If the resultant of all external forces is zero, then velocity of centre of mass will be

Accepted Answer

$F_{external}= M   a_{CM}$   where M is the total mass.Zero net external force implies that $a_{CM}= 0$Thus   $V_{CM} = constant$  OR zero(If the system is at rest initially,  then $V_{CM}= 0$)

Question 6

When the velocity of a body is doubled

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

Geometric centre

Question 9

The motion of centre of mass depends on

Accepted Answer

The motion of centre of mass depends only on the net external force.Let M be the total mass.$\vec{F}_{external} = M\vec{a}_{CM}$

Question 10

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

Accepted Answer

$Couple$ 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.

Systems Of Particles And Rotational Motion

Physics
8841 Views

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:

The centre of a mass of a rigid body lies

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

If the resultant of all external forces is zero, then velocity of centre of mass will be

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 _____.

The motion of centre of mass depends on

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

Systems Of Particles And Rotational Motion

Physics 8841 Views

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:

The centre of a mass of a rigid body lies

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

If the resultant of all external forces is zero, then velocity of centre of mass will be

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 _____.

The motion of centre of mass depends on

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

Physics
8841 Views

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