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The centre of mass of a system of particles is at the origin. Which of the following statement is incorrect . The number of particle to the righ of the origin is equal to the number of particles to the left The total mass of the particles to the right of the origin is same as the total mass to the left of the origin The number of particles on X-axis should be equal to the number of particles on Y-axis If there is a particle on the positive X-axis, there must be at least one particle on the negative X-axis.

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A rocket of mass 4000 kg is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude 19.6 m/s2 . [Exhaust speed of fuel = 980 m/s.]. (1) 240 kg s –1  (2) 60 kg s –1  (3) 120 kg s –1  (4) 130 kg s –1 

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A balloon having mass 'm' is filled with gas and is held in hands of a boy. Then suddenly it gets released and gas starts coming out of it with a constant rate. The velocity of the ejected gas is 2m/s with respect to the balloon. Find out the velocity of the balloon when the mass of gas is reduced to half :( neglect gravity) ln2 2ln4 2ln2 None of these

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A wagon filled with sand has a hole so that sand leaks through the bottom at a constant rate λ. An external force 𝐹 ⃗ acts on the wagon in the direction of motion. Assuming instantaneous velocity of the wagon to be 𝑉 ⃗ and initial mass of system to be m0, the force equation governing the motion of the wagon is 𝐹 ⃗ = 𝑚_0 (𝑑𝑉 ⃗" " )/𝑑𝑥 + λ𝑉 ⃗ 𝐹 ⃗ = 𝑚_0 (𝑑𝑉 ⃗" " )/𝑑𝑥 - λ 𝑉 ⃗ 𝐹 ⃗ = (𝑚_0−"λ " 𝑡)(𝑑𝑉 ⃗" " )/𝑑𝑥 (𝑚_0−"λ " 𝑡)(𝑑𝑉 ⃗" " )/𝑑𝑥 + λ 𝑉 ⃗

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The carriage of mass M has constant initial velocity u along a straight horizontal track when at t=0. it starts raining. The rain drops have a vertical velocity u′ and result into addition of mass in per second to the carriage. The velocity of ear after T second of start of rain is (Asume frictionlews surface): see the sheet

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An open water tight railway wagon of mass 5 × 〖"10" 〗^"3" kg coasts at an initial velocity 1.2 m/s without friction on a railway track. Raindrops fall vertically down wards into the wagon. The velocity of the wagon after it has collected 〖"10" 〗^"3" kg of water will be 0.5 m/s  (B) 2 m/s  (C) 1 m/s  (D) 1.5 m/s

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A bead of mass m and diameter d is sliding back and forth with velocity v on a wire held between two right walls of length L. Assume that th ecollisions with the wall are perfectly elastic and there is no friction. The average force that the bouncing bead exerts on the one of the walls is : mv^2/(𝑙−𝑑) mv^2/(𝑙+𝑑) 〖2mv〗^2/(𝑙−𝑑) 〖2mv〗^2/(𝑙+𝑑)

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A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest . The kinetic energy of the balls after the collision is three fourths of the original . Find the coefficient of restitution 1. 𝑣/(√3) 2. √3 3. (√3)/(√2) 4. (√2)/(√3)

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A mass m moves with a velocity v and collides in-elastically with another identical mass at rest . After collision the first mass moves with velocity 𝑣/(√3) in a direction perpendicular to the initial direction of motion . Find the speed of second mass after collision 2𝑣/(√3) 𝑣/(√3) (𝑣√2)/(√3) The situation of the problem is not possible without external impulse

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Two bodies A and B , collide as shown in figures a and b below .circle the true statement : (a) (b) They exert equal and opposite forces on each other in (a) but not in (b) They exert equal and opposite forces on each other in (b) but not in (a) They exert equal and opposite forces on each other in (a) and (b) The forces are equal and opposite to each others in a but only the component of the forces parallel to the velocities are equal in b .

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A particle is projected from a smooth horizontal surface with velocity v at an angle 𝜃 from horizontal . Coefficient of restitution between the surface and ball is e . The distance of the point where ball strikes the surface second time from the point of projection is . (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^2))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^4))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^3))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 𝑒))/𝑔

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