Q: A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

\textbf{Step 1: Energy Conservation [Ref. Fig.]} \text{Dependence on m} Let u be the minimum speed required at B .Apply energy conservation between point A and B we get KE_A + PE_A = KE_B + PE_B Taking point A as zero potential level \Rightarrow \dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} mv^2 ....(1) From equation 1 , we observe that mass m is cancelled on both sides. \Rightarrow u is independent of m . \textbf{Steo 2: Solving Equation} \text{Dependence on R} At highest point, Tension will be zero for minimum velocity \Rightarrow gravitational pull will provide necessary centripetal force \Rightarrow mg = \dfrac{mv^2}{R} \Rightarrow v^2 = Rg .... Putting in equation (1) We get, \dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} m (Rg) \Rightarrow u = \sqrt{5Rg} \Rightarrow u is proportional to the square root of R .Hence option B is correct.

Question 1

In which of the following cases the net force is not equal to zero?

Accepted Answer

As ball is falling freely that means weight of ball is acting on it hence net force is not zero and in all other cases things are stationary so net force on them is zero.

Question 2

Maximum value of static friction is:

Accepted Answer

Static friction is the friction acting on a body when the body is not in motion, but a force is acting on it. Static friction is the same as the force being applied (because the body isn't moving). Limiting friction is the friction on a body just before it starts moving.

Question 3

Impulse is equal to

Accepted Answer

Impulse   (\vec{J})   is defined as the change in the momentum. 	herefore     \vec{J}  = \Delta \vec{P}   = m (\vec{v_2}  - \vec{v_1})

Question 4

A certain particle undergoes erratic motion. At every point in its motion, the direction of the particle's momentum is always

Accepted Answer

Linear momentum ( \vec{P} ) of a body of mass m and velocity  \vec{v}  is expressed as:   \vec{P}=m\vec{v} . Since,  \vec{P}  is a vector quantity and its direction is defined by the direction of  \vec{v} , it always has the same direction as  \vec{v} .

Question 5

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

Accepted Answer

extbf{Step 1: Energy Conservation     [Ref. Fig.]} 	ext{Dependence on m} Let  u  be the minimum speed required at  B .Apply energy conservation between point  A  and  B  we get               KE_A + PE_A = KE_B + PE_B Taking point  A  as zero potential level     \Rightarrow              \dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} mv^2     ....(1) From equation  1 , we observe that mass  m  is cancelled on both sides. \Rightarrow u  is independent of  m . 	extbf{Steo 2: Solving Equation} 	ext{Dependence on R} At highest point, Tension will be zero for minimum velocity \Rightarrow  gravitational pull will provide necessary centripetal force            \Rightarrow mg = \dfrac{mv^2}{R}             \Rightarrow v^2 = Rg  .... Putting in equation  (1) We get,  \dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} m (Rg)             \Rightarrow u = \sqrt{5Rg} \Rightarrow u  is proportional to the square root of  R .Hence option  B  is correct.

Question 6

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:
$(g = 10 m s^{- 2})$

Accepted Answer

Given:  m=0.6 kg; R=0.75 m Force equilibrium T=\dfrac{mv^{2}}{R}      =\dfrac{(0.6)(5)^{2}}{(0.75)}      =20 N

Question 7

Which of following Newton's laws reveals the underlying symmetry in the forces that occur in nature?

Accepted Answer

Newton's third law of motion states that all the forces in nature have an equal and opposite reaction force present. This explains the underlying symmetry in the forces that occur in nature.

Question 8

The quantity that best represents the motion of a rigid body is

Accepted Answer

Mass of a body is the quantity of inertia possessed by it, or in simpler words, it is the measure of resistance that a body can provide to change in its motion.Speed is the measure of how fast a body is moving.Velocity is the measure of how fast a body is moving along with its direction.Linear momentum is the quantity which denoted the motion of body along with its direction.

Question 9

Statement A: If the force varies with time then the net force is measured by the total change in momentum of the body.Statement B: Change in momentum and impulsive force are numerically equal.

Accepted Answer

Force is a rate of change of momentum. Force  is measured as  rate\ of\ change\ of\ momentum.  It is not equal to change of momentum. F=\dfrac{dM}{dt}     or,  F\cdot dt=dM Impuse of force,  J=F\cdot dt=dM Hence, Change in momentum and impulsive force are numerically equal.A is wrong and B is correct.

Question 10

When a moving body is suddenly stopped, then:

Accepted Answer

Frictional force arises when there is a relative motion between two surfaces. When body is stopped means there is no relative motion and no resultant force is there hence frictional force acting becomes zero.

Laws Of Motion

Physics
319 Views

In which of the following cases the net force is not equal to zero?

Maximum value of static friction is:

Impulse is equal to

A certain particle undergoes erratic motion. At every point in its motion, the direction of the particle's momentum is always

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:
$(g = 10 m s^{- 2})$

Which of following Newton's laws reveals the underlying symmetry in the forces that occur in nature?

The quantity that best represents the motion of a rigid body is

Statement A: If the force varies with time then the net force is measured by the total change in momentum of the body.
Statement B: Change in momentum and impulsive force are numerically equal.

When a moving body is suddenly stopped, then:

Laws Of Motion

Physics 319 Views

In which of the following cases the net force is not equal to zero?

Maximum value of static friction is:

Impulse is equal to

A certain particle undergoes erratic motion. At every point in its motion, the direction of the particle's momentum is always

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:(g=10ms−2)

Which of following Newton's laws reveals the underlying symmetry in the forces that occur in nature?

The quantity that best represents the motion of a rigid body is

Statement A: If the force varies with time then the net force is measured by the total change in momentum of the body. Statement B: Change in momentum and impulsive force are numerically equal.

When a moving body is suddenly stopped, then:

Physics
319 Views

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:
$(g = 10 m s^{- 2})$

Statement A: If the force varies with time then the net force is measured by the total change in momentum of the body.
Statement B: Change in momentum and impulsive force are numerically equal.