ADVANCE DEFENCE ACADEMY
LAWS OF MOTION ( SHEET 02)
Q1.An elevator and its load weigh a total of 800 kg. Find the tension T in the
supporting cable when the elevator, originally moving downwards at 20 m/s is
brought to rest with constant retardation in a distance of 50 m. (Ans. 1.104 x
10⁴ N)
Q2.A cricket ball of mass 150 g is moving with a velocity of 12 m/s and is hit
by a bat, so that the ball is turned back with a velocity of 20 m/s. The force of
the blow acts for 0.01 second on the ball. Find the average force exerted by
the bat on the ball. (Ans. 480 N)
Q3. A hammer of mass 1 kg strikes on the head of a nail (of negligible mass)
with a speed of 2m/s. It drives the nail 0.01 m into a wooden block. Find (i) the
force applied by the hammer, (ii) the time of impact and (iii) the impulse.
[Ans.(i)200 N; (ii)0.01s; (iii)-2 Ns]
Q4. Two billiard balls of mass 50 g moving in opposite directions with speed of
16~ms^{-1} collide and rebound with the same speed. What is the impulse
imparted by each ball to the other? (Ans.-1.6 kgm/s ,+1.6kgm/s)
Q5. A machine gun has a mass of 20 kg. It fires 30 g bullets at the rate of 400
bullets per second with a speed of 400 m/s. What force must be applied to the
gun to keep it in position? (Ans. 4800 N)
Q6. A ball of mass 20 g hits a wall at an angle of 45° with a velocity of 15 m/s.
If the ball rebounds at 90° to the direction of incidence, calculate the impulse
received by the ball.(Ans.0.42 kgm/s)
Q7. A ball moving with a momentum of 15 kg m/s strikes against the wall at an
angle of 30° and is reflected with the same momentum at the same angle.
Calculate impulse. (Ans.-15√3 kgm/s)
Q8. A body of mass 0.25 kg moving with velocity 12 m/s is stopped by applying
a force of 0.6 N. Calculate the time taken to stop the body. Also calculate the
impulse of this force. (Ans. 5 s, 3 Ns)
Q9. A 30 g bullet leaves a rifle with a velocity of 300 m/s and the rifle recoils
with a velocity of 0.6 m/s. Find the mass of the rifle. (Ans. 15 kg)
Q10. A 40 kg shell is flying at a speed of 72 km/h. It explodes into two pieces.
One of the two pieces of mass 15 kg stops. Calculate the speed of the other.
(Ans. 32 m/s)
Q11. A gun weighing 4 kg fires a bullet of 80 g with a velocity of 120 m/s. With
what velocity does the gun recoil? What is the combined momentum of the
gun and bullet before firing and after firing? (Ans. 2.4 cm/s; zero before and
after firing)
Q12. A car of mass 1000 kg moving with a speed of 30 m/s collides with the
back of a stationary lorry of mass 9000 kg. Calculate the speed of the vehicles
immediately after the collision if they remain jammed together. (Ans. 3 m/s)
Q13. A bullet of mass 7 g is fired into a block of metal weighing 7 kg. The block
is free to move. After the impact, the velocity of the bullet and the block is 70
cm/s. What is the initial velocity of the bullet ?(Ans. 700.7 m/s)
Q14. A truck of mass 2 x 10⁴kg travelling at 0.5 m/s collides with another truck
of half its mass moving in the opposite direction with a velocity of 0.4 m/s. If
the trucks couple automatically on collision, calculate the common velocity
with which they move. (Ans. 0.2 m/s.)
Q15. A bomb at rest explodes into three fragments of equal masses. Two
fragments fly off at right angles to each other with velocities 9 m/s and 12 m/s
respectively. Calculate the speed of the third fragment. (Ans. 15 m/s)
Q16. A rocket with a lift mass of 3.5 x 10⁴kg blasted upwards with an
acceleration of 10 m/s². Calculate the initial thrust of the blast. (Ans. 7.0 x 10⁵
N)
Q17. Fuel is consumed at the rate of 50 g per second rocket. The exhaust
gases are rejected at the rate of 5 x 10⁵ cm/s. What is the thrust experienced
by the rocket ? (Ans. 250 N)
Q18. A rocket motor consumes 100 kg of fuel per second, exhausting it with a
speed of 6 x 10³ m/s. What. (i) thrust is exerted on the rocket ? (ii) What will
be the velocity of the rocket at the instant its mass is reduced to (1/40)th of
its initial mass, its initial velocity being zero?
Neglect gravity. [Ans. (i) 6 x 10⁵N (ii) 22.13 x 10³
m/s]
Q19. A mass of 6 kg is suspended by a rope of
length 2 m from a ceiling. A force 50N in the
horizontal direction is applied at the midpoint of
the rope as shown in Fig. 5.29. What is the angle
that rope makes with the vertical in equilibrium?
Take g=10 m/s². Neglect mass of the rope.[NCERT]
(Ans. Tan-¹(5/6))
Q20. A body of weight 200 N is suspended with the help of strings as shown in
Fig . Find the tensions T1 and T2.(Ans. T1=146.4N, T2=179.3N)
Q21. Two masses of 6 kg and 4 kg are connected to the two ends of a light
inextensible string that goes over a fixed frictionless pulley. Find the
acceleration of the masses and the tension in the string when the masses are
released. Take g=10m/s² [Ans. 2m/s²; 24 N)
Q22. Two masses m1 and m2 are connected by a massless string as shown in
Fig . Find the value of tension in the string if a force of 200 N is applied on :
(I) m1 and (ii) m2. [Ans. (1) 75 N (ii) 125 N]
Q23. In Fig., find the acceleration a of the system and the tensions T1 and T2
in the strings. Assume that the table and the pulleys are frictionless and the
strings are massless. Take g=9.8 m/s² (Ans. 1.4 m/s²; 22.4 N, 33.6 N)
Q24. Three bodies A, B and C, each of mass m are hanging on a string over a
fixed pulley, as shown in Fig. What are the tensions in the strings connecting
bodies A to B and B to C? ( Ans. .4/3mg, 2/3mg)
Q25. A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined
until at an angle 15° with the horizontal, the mass just
begins to slide. What is the coefficient of static friction
between the block and the surface? [NCERT]( Ans. 0.27)
Q26. A body rolled on ice with a velocity of 8 m/s comes to
rest after travelling 4 m. Compute the coefficient of friction. Given g=9.8 m/s²
(Ans. 0.8164)
