A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

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Initial momentum of the system (parent nucleus) = 0

Let v₁ and v₂ be the respective velocities of the daughter nuclei having masses m₁ and m₂.

Total linear momentum of the system after disintegration = m₁v₁ + m₂v₂ 

According to the law of conservation of momentum, 

Total initial momentum = Total final momentum 

                                 0 = m₁v₁ + m₂v₂ 

                                v₁ = -m₂v₂ / m₁ 


Here, the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.

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When we push or pull the lawn mower with force F at angle θ with horizontal, the force of push or pull can be resolved into two rectangular components:
(i) F cosθ, the horizontal component which helps it to move in forward direction.
(ii) F sinθ, the vertical component of force.

In case of pull, F sinθ acts in vertically upward direction which decreases the normal reaction and hence force of friction decreases.
Since in case of pull, force of friction is less than that in the case of push, hence it is easy to pull than to push.

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Mass of each ball, m = 0.05 kg 

Initial velocity of the ball = 6 m/s 

Magnitude of the initial momentum of the ball, p₁ = 0.05 x 6

    = 0.3 kg m/s

After collision, the balls change their directions of motion without changing the magnitudes of their velocity.

Final momentum of each ball, p_f = - 0.3 kg m/s

Impulse imparted to each ball = p_f - p_i = -0.3 -0.3 = -0.6 kg m/s

The negative sign indicates that the impulses imparted to the balls are opposite in direction.

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The acceleration of the belt results in pseudo force acting on the man and is equal to mass times the acceleration of the belt opposite to the direction of belt.

i.e.           F = ma =65 x 1 = 65N

The man will continue to be stationary on the belt till the pseudo force on the man is less or equal to limiting friction.

i.e.            

             

                 

Here ,

Therefore, 
                   

Hence,  the maximum acceleration with which the belt can accelerate is 

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Mass of body A, m₁ = 10 kg

Mass of body B, m₂ = 20 kg

Total mass of the system, m = m₁ + m₂ = 30 kg

Using Newton’s second law of motion,

                        F = ma 

Acceleration (a) produced in the system can be calculated as, 

          = 

When force is applied on a body A. 

Equation of motion can be written as, 

F - T = m₁a

Therefore,

T = F - m₁a

   = 600 - 10 x 20

   = 400 N                                ...  (i)

When Force is applied on a body B, we have 

F - T = m₂a

i.e., T = F - m₂a 

Therefore, 

T = 600 - 20 x 20 = 200 N         ... (ii)

From (i) and (ii), we can say that the answer is different in both the cases. 

Therefore, the answer depends on which end of mass, the force is applied.