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

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Laws Of Motion

Q: A fly-over bridge is a part of a vertical circle of radius \$80\ m\$ and a vehicle is travelling on it. The vehicle does not leave the surface of bridge at its highest point, if maximum speed of vehicle is:

For the vehicle not to leave the surface, it has to travel with critical velocity. So, \$v =\sqrt{gR}\$ \$=\sqrt{9.8\times80}\$ \$=\sqrt{784}\$or, \$v =28\ ms^{-1}\$

Q: 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):

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.

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

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.

Q: When a moving body is suddenly stopped, then:

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.

Q: When a body is in equilibrium, which of the following must be true ?

A body is in equilibrium only when there is no net external force acting on it. So, in other words, the sum of all forces acting on it must be zero for a body to be in equilibrium.

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

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.

Physics
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JEE Mains JEE Advanced NEET AIIMS BITSAT Easy Qs Med Qs Hard Qs

A fly-over bridge is a part of a vertical circle of radius $80 m$ and a vehicle is travelling on it. The vehicle does not leave the surface of bridge at its highest point, if maximum speed of vehicle is:

14 m / s

21 m / s

28 m / s

42 m / s

Easy

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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):

m (u + v)

towards the wall

m (u - v)

towards the wall

m (u + v)

away from the wall

m (u - v)

away from the wall

Easy

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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.

A & B are correct

A & B are wrong

A is correct and B is wrong

A is wrong and B is correct

Easy

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

First law

Second law

Third law

Law of gravitation

Easy

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When a moving body is suddenly stopped, then:

Frictional force increases.

Friction force remains same as it was while the car was moving.

Friction force reduces but has a non zero value.

Frictional force reduces to zero as it is a self adjusting force.

Easy

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When a body is in equilibrium, which of the following must be true ?

There is no force acting on it.

The sum of all the forces acting on it must be zero.

The sum of all the forces acting on it is not equal to zero.

There are exactly two forces acting on the body.

Easy

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Impulse is equal to

momentum

change in momentum

rate of change of momentum

rate of change of force

Easy

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Assertion

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

Reason

It is due to inertia of rest.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion is correct but Reason is incorrect

Assertion is incorrect but Reason is correct

Easy

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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 :

decreases with increasing the mass of the stone

is independent of the mass of the stone

decreases with increasing the length of the string

is independent of the length of the string

Easy

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

A kite skillfully held stationary in the sky.

A ball falling freely from a height.

A helicopter hovering above the ground.

A cork floating on the surface of water.

Easy

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Laws Of Motion

Physics 6396 Views

A fly-over bridge is a part of a vertical circle of radius 80 m and a vehicle is travelling on it. The vehicle does not leave the surface of bridge at its highest point, if maximum speed of vehicle is:

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):

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:

When a body is in equilibrium, which of the following must be true ?

Impulse is equal to

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

It is due to inertia of rest.

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 :

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

Physics
6396 Views

A fly-over bridge is a part of a vertical circle of radius $80 m$ and a vehicle is travelling on it. The vehicle does not leave the surface of bridge at its highest point, if maximum speed of vehicle 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.