Two balls, having linear momenta p → 1 = p i ^ and p → 2 = - p i ^ , undergo a collision in free space. There is no external force acting on the balls. Let p → 1 ' and p → 2 ' be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of p , a 1 , a 2 , b 1 , b 2 , c 1 and c 2 .

p → 1 ' = a 1 i ^ + b 1 j ^ p → 2 ' = c 2 k ^

p → 1 ' = c 1 k ^ p → 2 ' = c 2 k ^

p → 1 ' = a 1 i ^ + b 1 j ^ + c 1 k ^ p → 2 ' = a 2 i ^ + b 2 j ^ - c 1 k ^

A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

Such that it escapes to infinity

In a circular orbit of a different radius

In the same circular orbit of radius R

This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M . If the maximum energy loss possible is given as f 1 2 m ν 2 then f = m M + m . Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Statement- I is false, Statement- II is true.

Statement- I is true, Statement- II is false.

Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- I .

Statement- I is true, Statement- II is true, Statement- II is not a correct explanation of Statement- I .

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A mass of $10 gm$ moving horizontally with a velocity of $100 cm \sec^{- 1}$ strikes the bob of a pendulum and sticks to it. The mass of the bob is also $10 gm$ . The maximum height to which the system can be raised is $(g = 10 m \sec^{- 2})$

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Important Questions on Centre of Mass, Momentum and Collisions

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 14

A solid iron ball

A

of radius

r

collides head-on with another stationary solid iron ball

B

of radius

2 r .

The ratio of their speeds just after the collision

(e = 0.5)

is :

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 15

Two balls, having linear momenta

{\vec{p}}_{1} = p \hat{i}

and

{\vec{p}}_{2} = - p \hat{i}

, undergo a collision in free space. There is no external force acting on the balls. Let

{\vec{p}}_{1}^{'}

and

{\vec{p}}_{2}^{'}

be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of

p, a_{1}, a_{2}, b_{1}, b_{2}, c_{1}

and

c_{2}

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 16

Assertion: A sphere of mass $m$ moving with speed $u$ undergoes a perfectly elastic head-on collision with another sphere of heavier mass $M$ at rest $(M > m)$ , then the direction of the velocity of the sphere of mass $m$ is reversed due to collision [no external force acts on a system of two spheres]

Reason: During a collision of spheres of unequal masses, the heavier mass exerts more force on lighter mass in comparison to the force which lighter mass exerts on heavier mass.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 17

Assertion: If the mass of the colliding particles remains constant, then the linear velocity of the individual particles change during collision along common normal direction.

Reason: A pair of equal and opposite impulses act along common normal direction.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 19

Assertion : A shell at rest, explodes. The centre of mass of fragments moves along a straight path.

Reason : In explosion the linear momentum of the system remains always conserved.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 20

Assertion: The centre of mass of a two-particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason: Product of mass of one particle and its distance from the centre of mass is numerically equal to the product of the mass of other particle and its distance from the centre of mass.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 21

Assertion: The centre of mass of a body may lie where there is no mass.
Reason: Centre of mass of a body is a point, where the whole mass of the body is supposed to be concentrated.

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 22

Assertion : Position of centre of mass is independent of the reference frame:
Reason: Centre of mass is same for all bodies.

A mass of 10 gm moving horizontally with a velocity of 100 cm sec-1 strikes the bob of a pendulum and sticks to it. The mass of the bob is also 10 gm. The maximum height to which the system can be raised is g=10 m sec-2

Important Questions on Centre of Mass, Momentum and Collisions

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A mass of $10 gm$ moving horizontally with a velocity of $100 cm \sec^{- 1}$ strikes the bob of a pendulum and sticks to it. The mass of the bob is also $10 gm$ . The maximum height to which the system can be raised is $(g = 10 m \sec^{- 2})$