Test: Newton's laws of Motion (June 2) - JEE MCQ

• The stone is moving in a circular path with constant speed, this is uniform circular motion.
• In uniform circular motion, at any instant velocity (magnitude speed) acts tangentially to the circular path.
• Hence, when string is cut the stone will fly off tangentially to circular path with velocity of magnitude speed.

Mass of the man, m = 70 kg
Acceleration, a = 0
Using Newton’s second law of motion, We can write the equation of motion as, 
R – mg = ma
∴ R = mg = 70 × 10 = 700 N
∴ the weighing scale = 700 / g = 700 / 10 = 70 kg

• The third law states that all forces between two objects exist in equal magnitude and opposite direction. 
• If one object A exerts a force F_A on a second object B, then B simultaneously exerts a force F_B on A, and the two forces are equal in magnitude and opposite in direction, F_A = −F_B
• Newton's third Law:
  

• Force is required to start a stationary object and to stop a moving object due to inertia. 
• Inertia is a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.
• This is also called law of inertia or newton's first law of motion.
• Newton's first Law:
  

• When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
• To every action there is always opposed an equal reaction or the mutual actions of two bodies upon each other are always equal and opposite in direction.

If net force act on a body then acceleration of the body will also be zero. Hence velocity will not be changed i.e. it continues in its existing state of rest or uniform motion in a straight line.

Weight of the stone is balanced by the reaction of the floor. The only acceleration is provided by the horizontal motion of the train.

a = 1ms^-2

Force in horizontal direction 

F = ma = 0.1 x 1 = 0.1N

According to Newton's second Law of motion,
Apparent weight, R = m(a+g) 

= 70(10+10) 

= 1400N 

mass = R/g

= 1400/10 

= 140Kg

• The moving helicopter is a non-inertial frame and hence we do need to apply pseudo force onto the body so as to solve equations with Newton's laws. 
• The pseudo force needed to be applied, f = ma = 300 x 15 N = 4500N
• Thus the net downward force due to the passengers is 7500N.

Given:

We have to  find the least force required to make the body slide.