Q: 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.

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.

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.

Q: Impulse is equal to

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

Question 1

The combined effect of mass and velocity is taken into account by a physical quantity called:

Accepted Answer

The force required to stop a moving body   depends on the velocity as well as its mass. This combined  quantity of mass and velocity is defined as momentum.$Momentum = mass \times velocity$$\overrightarrow{P} = m \times \overrightarrow{v}$

Question 2

A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):

Accepted Answer

A ball of mass, m, moving with initial velocity, u to the right towards a wall. It will have momentum $\overrightarrow { { p }_{ i } } =m\overrightarrow { u } $ towards the right.The ball bounces off the wall. It will now be moving to the left, with the same mass, but a different velocity, v and therefore, a different momentum,$\overrightarrow { { p }_{ f } } =m\overrightarrow { v } $ towards the left.The final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, $\triangle \overrightarrow { p } =m\overrightarrow { \triangle v }$ .  Using tail to head vector addition, $\triangle \overrightarrow { p }$, must be the vector that starts at the head of $ \overrightarrow { { p }_{ i } }$ and ends on the head of $\overrightarrow { { p }_{ f } }$, hence the resultant change in momentum vector will point towards the left, that is, away from the wall.We also know from algebraic addition of vectors that:$\overrightarrow { { p }_{ f } } =\overrightarrow { { p }_{ i } } +\triangle \overrightarrow { p } \ $$\overrightarrow { { p }_{ f } } -\overrightarrow { { p }_{ i } } =\triangle \overrightarrow { p }$Magnitude of the change in momentum = $m v-(-u)=m(v+u)$Direction of change in momentum is towards the left, away from the wall.

Question 3

When an athlete takes part in a long jump he runs for a while and then jumps. This is because:

Accepted Answer

The inertia helps him to retain his horizontal speed and hence the athlete can jump with a greater horizontal velocity to cover a longer distance.

Question 4

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 5

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 6

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.

Question 7

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

$\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 8

Impulse is equal to

Accepted Answer

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

Question 9

When a bus starts suddenly, a person standing in it falls backwards.

Accepted Answer

It is due to inertia of rest.

Question 10

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.

Laws Of Motion

Physics
8095 Views

The combined effect of mass and velocity is taken into account by a physical quantity called:

A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):

When an athlete takes part in a long jump he runs for a while and then jumps. This is because:

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.

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

When a moving body is suddenly stopped, then:

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 :

Impulse is equal to

When a bus starts suddenly, a person standing in it falls backwards.

It is due to inertia of rest.

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

Laws Of Motion

Physics 8095 Views

The combined effect of mass and velocity is taken into account by a physical quantity called:

A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):

When an athlete takes part in a long jump he runs for a while and then jumps. This is because:

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.

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

When a moving body is suddenly stopped, then:

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 :

Impulse is equal to

When a bus starts suddenly, a person standing in it falls backwards.

It is due to inertia of rest.

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

Physics
8095 Views

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.