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 semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in the figure. The distance of centre of mass $C$ of remaining plate from point $O$ is:

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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 9

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles and each of the two line segments is $m$ . The mass of the ink used to draw the outer circle is $6 m$ . The coordinates of the centres of the different parts are: outer circle $(0, 0)$ ; left inner circle $(- a, a)$ , right inner circle $(a; a)$ , vertical line $(0, 0)$ and horizontal line $(0, - a)$ . The $y$ -coordinate of the centre of mass of the ink in this drawing is

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 10

A radioactive nucleus initially at rest decays by emitting an electron and neutrino at right angles to one another. The momentum of the electron is $3.2 \times 10^{- 23} kg m s^{- 1}$ and that of the neutrino is $6.4 \times 10^{- 23}$ $kg m s^{- 1}$ . The direction of the recoiling nucleus with that of the electron motion is,

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 11

A particle of mass

1 kg

is thrown vertically upwards with a speed of

100 m / s

. After

5 s

, it explodes into two parts. If one part of mass

400 g

comes back with speed

25 m / s,

then the speed of other part just after explosion is

(Take g = 10 m s^{- 2})

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 12

A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After collision, the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after collision:

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Alpha Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise-2>Q 13

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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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.

A semicircular portion of radius r is cut from a uniform rectangular plate as shown in the figure. The distance of centre of mass C of remaining plate from point O is:

Important Questions on Centre of Mass, Momentum and Collisions

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A semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in the figure. The distance of centre of mass $C$ of remaining plate from point $O$ is: