Momentum, K.E. Relation

Q.

The distance of the closest approach of an alpha-particle fired towards a nucleus with momentum $p$ is$r.$ If the momentum of the alpha-particle is $2p$, the corresponding distance of the closest approach is

1. $4r$

2. $2r$

3. $\frac{r}{2}$

4. $\frac{r}{4}$

Q.

A light body and a heavy body have the same kinetic energy. Which one will have greater momentum?

Q.

A particle of mass $m$ is moving along the x-axis with an initial velocity $u\hat{i}$. It collides elastically with a particle of mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \left({\theta }_1\right)=\sqrt{n}\sin \left({\theta }_2\right)$ then value of $n$ is

Q. Statement -1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement -2 : Principle of conservation of momentum holds true for all kinds of collisions.

1. Statement -1 is ture , statement -2 is true, and statement-2 is correct explanation of statement -1.
2. Statement-1 is ture, statement-2 is true, but statement -2 is not a correct explanation of statement-1.
3. Statement-1 is false, but statement-2 is true.
4. Statement-1 is true, but statement -2 is false.

Q.

What happens to the momentum when two objects collide?

Q.

Is momentum always conserved?

Q. State TRUE or FALSE for given STATEMENTS , Give REASON for FALSE statement :
(i) Total mechanical energy is always conserved in collision .
(ii) Kinetic energy is always conserved in collisions .
(iii) Velocity before and after collision of respective bodies remain same .
(iv) Total momentum is always conserved in collisions .

Q. Two ice skaters A and B approach each other at right angles. Skater A has a mass $30\text{kg}$ and velocity $1\text{m/s}$ skater B has a mass $20\text{kg}$ and velocity $2\text{m/s}$. They meet and cling together. The final velocity of the couple is

1. $2\text{m/s}$
2. $1.5\text{m/s}$
3. $1\text{m/s}$
4. $1.5\text{m/s}$

Q. A bullet of mass $20\text{g}$ and moving with $600\text{m/s}$ collides with a block of mass $4\text{kg}$ hanging with the string. What is velocity of bullet when it comes out of block, if block rises to height $0.2\text{m}$ after collision?
(Take $g=10{\text{m/s}}^2$)

1. $200\text{m/s}$
2. $150\text{m/s}$
3. $400\text{m/s}$
4. $300\text{m/s}$

Q. A rigid body rotates with an angular momentum $L$ . If its rotational kinetic energy is made 4 times, its momentum will become

1. 4 $L$
2. 16 $L$
3. $\sqrt{2}$ $L$
4. 2$L$

Q.

Consider a head-on collision between two particles of masses $m_1$ and $m_2$.The initial speeds of the particles are $u_1$ and $u_2$ in the same direction.The collision starts at t=0 and the particles interact for a time interval $△t$.During the collision, the speed of the first particle varies as

$v\left(t\right)=u_1+\frac{t}{△t}(v_1-u_1).$

Q.

When a bomb explodes in mid-air , its

1. momentum increases

2. Momentum remains constant

3. Kinetic energy increases

4. Kinetic energy remains constant

Q. What is the partial safety factor for dead load when it contributes to the stability of the structure against overturing?

1. 1
2. 1.5
3. 1.2
4. 0.9

Q. A particle of mass $1\text{kg}$ suffers one - dimensional elastic collision with an unknown mass at rest. It is scattered directly backward by losing $64\%$ of its initial kinetic energy. The unknown mass $\left(\text{in kg}\right)$ is

Q. A 2 kg mass moving with a velocity of $10m{s}^{-1}$ collides with another 6 kg mass moving in opposite direction with a velocity of $20m{s}^{-1}$. After the collision, they stick and move together. Their common velocity is m/s and the momentum is kg m/s.

1. 12.5
2. 7.5
3. 50
4. 100

Q. For an perfectly inelastic collision, which of the following holds true.

1. Momentum of the system is always conserved.
2. Velocity of separation is not equal to the velocity of approach.
3. Kinetic energy of the system is not conserved.
4. All the above

Q.

A molecule in a gas container hits a horizontal wall with speed 200 m s^–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

Q. Two balls of masses, $3\text{kg}$ and $5\text{kg}$ are moving as shown in the figure. After the collision, both the balls moves together. Their common velocity after collision is -

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $3\text{m/s}$
4. $4\text{m/s}$

Q.

Can a single object have kinetic energy but no momentum? Can a system of two or more particles have kinetic energy but no momentum? Explain your answer.

Q.

A particle can have non-zero kinetic energy and zero momentum.

1. True
2. False

Q. A $250\text{gm}$ grasshopper moving due south at $20\text{cm/s}$ (in mid air) collides with another $150\text{gm}$ grasshopper moving at a speed of $60\text{cm/s}$ due north. Find the decrease in KE if they move together after collision.

1. $0.3\text{J}$
2. $3.0\text{J}$
3. $0.003\text{J}$
4. $0.03\text{J}$

Q.

The conservation of linear momentum can be applied in one direction while at the same time it can’t be applied in other directions.

1. True
2. False

Q. Discuss elastic collision in two dimension.

Q.

The kinetic energy of a body of mass $15kg$ is $30J$. What is its momentum? $(UseK.E=\frac{p^2}{2m}).$

Q. A blast breaks a body of mass $0.5\text{kg}$, initially at rest, into three pieces, two smaller pieces of equal masses and the third having double the mass of either of the small pieces. After the blast, the two smaller masses move at right angles to one another with equal speed. Find the statement(s) that is/are true for this case assuming that the energy of the blast is totally transferred to the masses.

1. All the three pieces share the energy of the blast equally.
2. The speed of the bigger mass is $\sqrt{2}$ times the speed of either of the smaller masses.
3. The direction of motion of the bigger mass makes an angle of ${135}^{\circ }$ with the direction of the smaller pieces.
4. The bigger piece carries double the energy of either smaller piece.

Q. A $250\text{gm}$ grasshopper moving due south at $20\text{cm/s}$ (in mid air) collides with another $150\text{gm}$ grasshopper moving at a speed of $60\text{cm/s}$ due north. Find the decrease in KE if they move together after collision.

1. $0.3\text{J}$
2. $3.0\text{J}$
3. $0.03\text{J}$
4. $0.003\text{J}$

Q. A body of mass $100\text{g}$ has a kinetic energy of $5\text{J}$. Find its linear momentum.

1. $8\text{kg-m/s}$
2. $4\text{kg-m/s}$
3. $2\text{kg-m/s}$
4. $1\text{kg-m/s}$

Q. Sir in ktg pressure derivation why we take time taken between two successive collisions instead of one collisions?

Q.

During an inelastic collision there is loss of kinetic energy of the system then why there is no loss in total momentum of the system ?

Q. Two masses, $m_1$ and $m_2$ were moving in opposite direction with speeds of $20\text{m/s}$ and $10\text{m/s}$ respectively. They collide and $m_1$ moves with $15\text{m/s}$ after collision in its same direction as of before collision. What is the speed and direction of the second particle after collision, if the coefficient of restitution is $2/3?$

1. $35\text{m/s}$ in same direction as of first particle
2. $20\text{m/s}$ in same direction as of first particle
3. $35\text{m/s}$ in opposite direction as of first particle
4. $20\text{m/s}$ in opposite direction as of first particle