When a constant force is applied to a body, it moves with uniform
Solution:
From Newton's second law of motion, F= m.a
if force is constant acceleration remains constant.
Question 1:
Linear Momentum and Second Law of Motion
Question 2:
A particle is moving with a constant speed along a straight line path. A force is not required to
Solution:
As the particle moves with constant speed in straight line its velocity is constant i.e accleration is zero. From Newton's second law of motion
F=m.a
Force required to keep moving with uniform velocity is zero.
Question 3:
A fireman wants to slide down a rope. The rope can bear a tension of (3/4)th of the weight of the man. With what minimum acceleration should the fireman slide down:
Solution:
According to the question, T=3mg/4
Using equations of motion, i.e. Fnet = m.a
⇒mg-T =ma
⇒mg-3mg/4= ma
⇒a =g/4
Question 4:
Consider the following two statements:
(A) Linear momentum of a system of particles is zero
(B) Kinetic energy of a system of particles is zero
Then:
Solution:
When kinetic energy of the system is zero, speed of objects will be zero so momentum will always be zero.
Whereas momentum being a vector quantity may be zero when directions of velocities cancel each other. so speed and kinetic energy may of may not be zero when momentum is zero
Question 5:
The linear momentum of a particle is given by P = a + bt², where t is time and a & b are constants. The force acting on the body is directly proportional to :
Solution:
Given momentum of the object is P = a + bt²;
Force is defined as rate of change of momentum F= dP/dt= 2bt. so Force is proportional to t.
Question 6:
A body of mass 1 kg moving on a smooth horizontal surface with velocity 5m/s is to be brought to rest in 5 sec. How much force need to be applied :
Solution:
Force is defined as rate of change of momentum ie. F= dP/dt= change in momentum / time
Here Force = (mv-mu)/t= m(v-u)/t= 1 kg (0- 5)/ 5 = 1 N
Question 7:
The momentum of a particle is P = 2cos tˆi + 2sin t ˆj. What is the angle between the force F acting on the particle and the momentum P ?
Solution:
Momentum of object is given as, P = 2cos tˆi + 2sin t ˆj ,
From Newtons Second law, F = dP/dt = -2 sin t î + 2 cos t ˆj.
Taking Dot product of P and F we get = -4 sint . cos t + 4 sint .cost =0 .
So, force and momentum are perpendicular to each other.
Question 8:
Two forces of 6N and 8N act on a body of mass 7 kg. The value of acceleration produced can not be more than :
Solution:
Maximum resultant force will act on the object when 6N and 8 N forces will be acting in same direction. F max= 14 N.
Maximum Acceleration= Maximum Force/ mass= 14 N/ 7 kg = 2m/s²
Question 9:
A body moving with uniform velocity is stopped in 0.25 sec by applying a force of 200 N. What is the impulse :
Question 10:
A rocket of mass 6000 kg is set for vertical firing. If the exhaust speed be 1 km/s how much gas must be ejected to give the rocket an upward acceleration of 20 m/s² (neglect gravity) :-
Solution:
According to Newtons second law of motion
F= v. dm/dt
so, acceleration = v. (dm/dt)/m
⇒ 20 m/s² = 1000 ×(dm/dt)/6000
⇒dm/dt = 120 kg/sec