Velocity of COM

Q.

According to the principle of conservation of momentum

1. When no external torque acts on a system of particles, then the total angular momentum of the system always remains constant.

2. When no external torque acts on a system of particles, then the total angular momentum of the system always remains zero.

3. When an external torque acts on a system of particles, then the total angular momentum of the system always remains zero.

4. When an external torque acts on a system of particles, then the total angular momentum of the system always remains zero.

Q. Two masses $m_1$ and $m_2$ are moving with velocities $v_1$ and $v_2$ respectively. Find their total kinetic energy in the reference frame of centre of mass.

1. $\frac{m_1{m}_2}{m_1+m_2}(v_1-v_2{)}^2$
2. $\frac{1}{2}\frac{m_1{m}_2}{m_1+m_2}(v_1-v_2{)}^2$
3. $\frac{1}{2}\frac{m_1{m}_2}{m_1+m_2}(v_1+v_2{)}^2$
4. $\frac{1}{2}\left(m_1{m}_2\right)(v_1-v_2{)}^2$

Q. A small block is sliding on a frictionless inclined plane that is moving upward with a cons†an t acceleration a. If the block remains at a cons†an t height from ground, then the acceleration of the inclined plane (Acceleration due to gravity is g) is

Q. Find the percentage decrease in acceleration due to gravity when a body is taken from the surface of earth to a height of 64 Km from its surface.

Q. what is rolling motion and kinetic energy of rolling motion?

Q. 24.a block of 10 kg mass is placed on a rough inclined surface as shown in the figure the acceleration of the block will be

Q. a uniform disk turns at 2.4rev/s around a frictionless axis.a non rotating rod , of the same mass as the disk and length equal to disks diameter is dropped onto the freely spinning disk.they then both turn around the axis with their centres superposed .what will be the angular frequency of the combination when they start rotating together.

Q. 35.A man of mass M stands on a platform of mass m and pulls himself up by pulley arrangement shown in the figure. If he pulls each rope with force F determine the upward acceleration

Q. Two identical balls of mass 2 kg each are kept in contact with a compressed spring, on either side of it.When the spring is released, the balls move with a velocity 10 ms^{-1}. Find the acceleration produced in each ball if the spring constant is 4 Nm^{-1}.

Q.

A nucleus moving with a velocity $\overrightarrow{v}$ emits an$\alpha$-p article. Let the velocities of the $\alpha$-particle and the remaining nucleus be $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ and their masses be $m_1$, and $m_2$.

1. , and must be parallel to each other.

2. + must be parallel to .

3. None of the two of , and should be parallel to each other.

4. must be parallel to .

Q. 95.Two particles each of mass m are released from rest from infinite separation. The velocity of any one when their separation becomes r will be?

Q. A super ball is to bounce elastically back and forth between two rigid walls at a dis†an ce d from each other.Neglecting gravity and assuming the velocity of super ball to be V horizontally, the average force being exerted by the super ball on one wall is how much

Q.

A block of mass m is pushed by applying a force F at an angle θ with the horizontal surface. The normal force on the block is given as -

1. F = mg

2. F = F sin θ

3. F = mg + F sin θ

4. F = mg - F sin θ

Q. A trolley is moving on a horizontal surface with constant acceleration A bob of mass m = 1 kg is suspended from the roof of trolley. What horizontal force F should be applied on the bob so that string makes an angle 60° with vertical in equilibrium w.r.t. trolley (g = 10 m/s2)

Q. state and Prove the principle of law of conservation of linear momentum

Q.

Two spheres of masses m1 and m2 (m1>m2) respectively are tied to the ends of a light, inextensible string which passes over a light frictionless pulley. When the masses are released from their initial state of rest, the acceleration of their centre of mass is:

1. 

2. 

3. 

4. 

Q. 29.A block of mass m is attached to a spring vertically.if spring is initially in its natural length and allowed to fall.Find the elongation in spring, when block will be in equilibrium and also find maximize elongation in spring? Explain with different possible cases also

Q. A smooth uniform solid sphere rolling without slipping with velocity Vo collides elastically and head on

Q.

One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h (figure). Initially, the spring makes an angle of ${37}^{\circ }$ with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.

1. 

2. 

3. 

4. None of these

Q. A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a verticle circular path about its other end. The minimum speed of the particle at its highest point must be- (a)zero (b) \sqrt{gl} (c) \sqrt{1.5gl} (d)\sqrt{2gl

Q. Two particles which are initially at rest, move towards each due to mutual attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be

1. $2v$
2. $1.5v$
3. $0$
4. $v$

Q. 58 A monkey of mass 10 kg is climbing up on an ideal rope which passes through an ideal pulley and on other side of rope a block of mass 11 kg is hanging. The acceleration of monkey w.r.ti ropes 1ms-2 upward.initially both monkey and mass were at rest. The force exerted by hinge on pulley is?

Q. a mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius r if the string does not slip on cylinder with what acceleration will the mass fall on release

Q. A spring of spring constant k suspends a block of mass m, find the maximum elongation of the spring when block is released from rest.

Q. State law of conservation of linear momentum and derive the law of conservation of linear momentum using newtons second law of motion.

Q. In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10-10 m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

Q. Use the definition of linear momentum from the previous question. Can we state the principle of conservation of linear momentum for a single particle?

Q. A block moving in air, explodes into two parts. Then just after explosion (neglect change in momentum due to gravity)

Statement $1$ :- The total momentum of the two parts must be equal to the momentum of the block before explosion.

Statement $2$ :- If no external force acts on a system, then the linear momentum of the system will be conserved.

1. Statement $1$ is true, Statement $2$ is true, Statement $2$ is the correct explanation for Statement $1$.
2. Statement $1$ is true, statement $2$ is true, statement $2$ is not the correct explanation for statement $1$.
3. Statement $1$ is true, but statement $2$ is false.
4. Statement $2$ is true, but statement $1$ is false.

Q. How to find the acceleration of center of mass of atwoods machine when the lighter body rises up with an acceleration a?

Q.

Three equal weights A, B and C of mass 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the figure The tension in the string connecting weights B and C is

1. 13 N

2. 3.3 N

3. 19.6 N

4. Zero