Physics - Systems Particles Rotational Motion - Quiz-7

A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two-point
masses m and 2m moving in the same horizontal plane with speeds 2v and v
respectively strike the bar as shown below in the figure and stick to the bar after the collision. Denoting angular velocity about the center of mass, total energy, and center of mass velocity of $ω$ , E and $v_{c}$ respectively, we have after collision

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$v_{c} = 2 m / s$
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$ω = \frac{3}{5} \frac{v}{a}$
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$ω = \frac{v}{5 a}$
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$E = \frac{2}{3} {mv}^{2}$

A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure. The ratio of inertia of the loop about x-axis to that about y-axis is:

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>1
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<1
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=1
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=1/2

Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then the moment of inertia of the system about an axis about one of the sides of the square is

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$M a^{2} + 2 M b^{2}$
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$M a^{2}$
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$M a^{2} + 4 M b^{2}$
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$\frac{8}{5} M a^{2} + 2 M b^{2}$

A body of mass (m) elastically collides with another stationary body of mass 3m. The fractional loss of K.E. of the body is:

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$\frac{8}{9}$
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$\frac{3}{4}$
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$\frac{3}{5}$
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$\frac{4}{7}$

A body of mass m slides down an incline and reaches the bottom with a velocity v. If the same mass were in the form of a ring which rolls down this incline, the velocity of the ring at bottom would have been

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v
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$\sqrt{2} v$
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$(1 / \sqrt{2}) v$
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$(\sqrt{2 / 5}) v$

A rod is released at an angle 45 $°$ to the horizontal as shown. If its length is L, its angular acceleration about its foot at ground is initially

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$\frac{3 g}{2 L}$
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$\frac{3 g}{\sqrt{2} L}$
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$\frac{3 g}{2 \sqrt{2} L}$
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$\frac{6 g}{\sqrt{2} L}$

The moment of inertia of pulley is I and its radius is R. The string doesn't slips on the pulley, as system is released, the acceleration of the system is

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$\frac{g}{(3 + \frac{I}{m R^{2}})}$
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$\frac{g}{(1 + \frac{I}{m R^{2}})}$
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$\frac{3 g}{(1 + \frac{I}{m R^{2}})}$
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$\frac{3 g}{(2 + \frac{I}{m R^{2}})}$

In uniform circular motion

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Both the angular velocity and the angular momentum vary
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The angular velocity varies but the angular momentum remains constant
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Both the angular velocity and the angular momentum stay constant
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The angular momentum varies but the angular velocity remains constant

A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 sec, it rotates through an angle θ₁. In the next 2 seconds, it rotates through an additional angle θ₂. The ratio of θ₂/θ₁ is:

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1
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2
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3
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5

A 100 g iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is

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10 N
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100 N
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1.0 N
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0.1 N

A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. By what velocity the gun rebounds backwards ?

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0.1 m/s
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10 m/s
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1 m/s
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0.01 m/s

A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of

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(1) 5 m/s
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(2) 0 m/s
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(3) 2.5 m/s
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(4) 3.0 m/s

In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is

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0.2 kg m sec^–1
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–0.2 kg m sec^–1
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0.1 kg m sec^–1
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–0.4 kg m sec^–1

A particle of mass m moving with velocity u makes an elastic one-dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F₀ linearly in time T/2 and decreases linearly to zero in further time T/2. The magnitude of F₀ is:

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mu/T
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2mu/T
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mu/2T
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None of these

A force of 50 dynes is acted on a body of mass 5 g which acts for an interval of 3 seconds, then impulse is

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0.15 × 10^–3 N-s
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0.98 × 10^–3 N-s
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1.5 × 10^–3 N-s
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2.5 × 10^–3 N-s

In an explosion a body breaks up into two pieces of unequal masses. In this

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Both parts will have numerically equal momentum
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Lighter part will have more momentum
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Heavier part will have more momentum
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Both parts will have equal kinetic energy

Two bodies of masses m₁ and m₂ have equal kinetic energies. If p₁ and p₂ are their respective momentum, then ratio p₁ : p₂ is equal to

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$m_{1} : m_{2}$
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$m_{2} : m_{1}$
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$\sqrt{m_{1}} : \sqrt{m_{2}}$
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$m_{1}^{2} : m_{2}^{2}$

A light and a heavy body have equal momenta. Which one has greater K.E

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The light body
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The heavy body
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The K.E. are equal
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Data is incomplete

A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is

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48 J
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32 J
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24 J
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288 J

If the K.E. of a body is increased by 300%, its momentum will increase by

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100%
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150%
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$\sqrt{300} %$
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175%

A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?

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The light body
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The heavy body
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Both have equal momentum
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It is not possible to say anything without additional information

Two bodies with kinetic energies in the ratio of 4 : 1 are moving with equal linear momentum. The ratio of their masses is

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1 : 2
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1 : 1
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4 : 1
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1 : 4

A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle is

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Less than that of the bullet
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More than that of the bullet
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Same as that of the bullet
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Equal or less than that of the bullet

A stationary particle explodes into two particles of masses m₁ and m₂ which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is

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m₁/m₂
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1
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m₁ v₂/m₂ v₁
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m₂/m₁

A bomb of mass 3.0 Kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s.The total energy imparted to the two fragments is

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(1) 07 kJ
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(2) 14 kJ
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(3) 2.4 kJ
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(4) 8 kJ

An object of mass 3m splits into three equal fragments. Two fragments have velocities $v \hat{j}$ and $v \hat{i}$ . The velocity of the third fragment is

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$v (\hat{j} - \hat{i})$
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$v (\hat{i} - \hat{j})$
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$- v (\hat{i} + \hat{j})$
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$\frac{v (\hat{i} + \hat{j})}{\sqrt{2}}$

A shell initially at rest explodes into two pieces of equal mass, then the two pieces will

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Be at rest
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Move with different velocities in different directions
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Move with the same velocity in opposite directions
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Move with the same velocity in same direction

Two solid rubber balls A and B having masses 200 gm and 400 gm respectively are moving in opposite directions with velocity of A equal to 0.3 m/s. After collision the two balls come to rest, then the velocity of B is

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0.15 m/sec
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1.5 m/sec
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–0.15 m/sec
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None of the above

A cannon ball is fired with a velocity 200 m/sec at an angle of 60° with the horizontal. At the highest point of its flight ,it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity

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100 m/s in the horizontal direction
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300 m/s in the horizontal direction
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300 m/s in a direction making an angle of 60° with the horizontal
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200 m/s in a direction making an angle of 60° with the horizontal

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

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(1) 15 m/s
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(2) 14.0 m/s
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(3) 7.0 m/s
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(4) 9.89 m/s

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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