Newton's Laws for System of Particles

Q. A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are

Q. Two particles P and Q describe shm of same period , same amplitude, along the same line about same equilibrium position O.When P and Q are on opposite sides of O at the same dis†an ce from O .When P and Q are on opposite sides of O at same d†an ce from O, they havee speed of 1.2m/s in same direction.When their displacements are same , they have same speed of 1.6m/s in oppte direction .The maximum velocity in m/ of either particles is

Q.

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the acceleration of the centre of mass of the two blocks.

1. 

2. 

3. 

4. g

Q.

The angular momentum of a body is 31.4 Js and its rate of revolution is 10 cycle per second. The momentum of inertia of the body about the axis of rotation is

1. 2.5 kgm²

2. 0.15 kgm²

3. 0.15 kgm²

4. 1.5 kgm²

Q. A U tube containing a liquid moves with horizontal acceleration g/2, and the separation between the limbs is d. The difference in their liquid levels.

Q. A ball hits the ground and loses 20% of its momentum. Coefficient of restitution is (1) 0.2 (2) 0.4 (3) 0.6 (4) 0.8

Q.

A disc of radius 'r' is removed from the disc of radius 'R' then

a. the minimum shift in centre of mass is zero

b. the maximum shift in centre of cannot be greater than $\frac{r^2}{(R+r)}$

c. Centre of mass must be lie where mass exists

d. the shift in centre of mass is $\frac{r^2}{(R+r)}$

1. b, c are correct

2. a, b, d are correct

3. a , b are correct

4. a, b, c, d are correct

Q. A body of mass 2kg is placed on a smooth horizontal surface .Two forces F1= 20N & F2=10√3N are acting on the body in direction making angle of 30 & 60 to the surface .The reaction of the surface on the body will be a)20N b)25N c)5N d)zero

Q.

Consider the following two statements:
(A) Linear momentum of the system remians constant.
(B) Centre of mass of the system remains at rest.

1. A implies B and B implies A.

2. A does not imply B and B does not imply A.

3. A implies B but B does not imply A.

4. B implies A but A does not imply B.

Q.

A 3.2 kg block starts at rest and slides a distance d down a frictionless 30. $0^{\circ }$ incline , where it runs into a spring . The block slides an addition 21.0 cm before it is brought to rest momentarily by compressing the spring , whose spring constant is 431 $\frac{N}{m}$

what is the value of d ?

1. 0.08m
2. 0.18m
3. 0.28m
4. 0.38m

Q.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_1$ and $m_2$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

1. 

2. g

3. 

4. 

Q. Give any 5 examples of impulses in our daily life with explanation.

Q.

A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two plates.

1. 

2. 

3. 

4. 

Q. Figure below shows a fixed wedge on which two blocks of masses 2 kg and 3 kg are placed on its smooth inclined surfaces. When the two blocks are released from rest, find the acceleration of centre of mass of the two blocks.

1. $\frac{\sqrt{31}g}{10}$
2. g
3. g/2
4. g/5

Q. 5. Two masses m1 and m2 are at infinite distance apart and initially at rest .What is their relative velocity of approach when the separation between them is r?

Q. A rifle bullets loses 1/20th of its velocity In passing through a plank. Assuming that the plank exerts a constant regarding force, the least number of such planks required just to stop the bullet is

Q. A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length l. The system is rotated about the other end of the spring with an angular speed omega in gravity free space. Find elongation in spring.

Q. A block of woof of mass 150g and density 0.8g/cc is immersed in water of density 1g/cc.Find the net upward force on the block and the upward acceleration.

Q. a body floats ina liquidvcontained in a beaker.The whole system as shown in the figure falls freely under gravity, the upthrust on the body i

Q. A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude
(a) mg
(b) mg/cosθ
(c) mg cosθ
(d) mg tanθ

Q. 7.2 particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. What is speed if each particle with respect to their centre of mass ?

Q. 89. Three particles of mass m are placed fixed at the corners of an equilateral triangle of length R\sqrt{}3. What is the value of escape speed of any mass from the centroid of the triangle?

Q. two particles of equal masses(m) each move in a circle of radius (r) under the action of their mutualgravitational attraction. find the time period of each particle

Q. 72.An object of mass m initially at rest slides down a smooth inclined plane with angle theta and height h. Find its final velocity.

Q. Two particles which are initially at rest move towards each under the action of their internal attraction . If their speeds are v and 2v any instant, then the speed of center of mass of the system will be ??

Q. 15 There is a uniform rod of mass m and lengthlhaving particles A of mass m and B of mass 3mattached at its end. The rod is hinged at a point sothat it can turn in a vertical plane about ahorizontal axis. Distance of hinge from particle A, so that angular acceleration of system is minimumwhen released from horizontal position is

Q. A body of mass m is placed on a smooth inclined plane making an angle θ withhorizontal. If the plane isgiven a horizontalacceleration a then whatwill be:(a)The acceleration of body(b)Normal reaction(cThe condition for the body to be at relative to the plane?

Q. A bomb kept at rest on a smooth horizontal surface, suddenly explodes then identify the correct statement:

1. $\text{COM}$ of bomb will remain at rest.
2. $\text{COM}$ of bomb will move along the surface with a constant velocity after the explosion.
3. After explosion, all the fragments of bomb will fly in vertically upwards direction.
4. Explosion of bomb will cause the centre of mass of bomb to accelerate.

Q.

Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momentum, then ratio $p_1:p_2$ is equal to

1. 

2. 

3. 

4. 

Q. if a plankof mass M is held firmly, a bullet of mass m moving with velocity v strikes it and peneterates a dis†an ce d in it. how far will the bullet peneterates if the plabk is free to mov