1. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be

2. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be

3. A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is

4. A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. The value of v is

5. A bus travelling the first one-third distance at a speed of 10 km/h, the next one-third at 20 km/h and the last one-third at 60 km/h. The average speed of bus is

6. A particle moves along the x-axis. The position x of the particle with respect to time t from the origin is given by x = b_0 + b₁t + b₂t². The acceleration of particle is

7. Motion of a particle is given by equation S=(3t³+7t²+14t+8) m. The value of acceleration of the particle at t=1 sec is

8. The motion of a particle along a straight line is described by equation: x = 8+12t−t³, where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is

9. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 sec, it covers a distance of

10. The velocity of train increases uniformly from 20 km/h to 60 km/h in 4 hours. The distance travelled by the train during this period is

11. The velocity of a bullet is reduced from 200ms^-1 to 100 ms^-¹ while travelling through a wooden plank of thickness 10 cm. The retardation, assuming it to be uniform, will be

12. A car moving with a speed of 40 km/h can be stopped by applying brakes after atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance?

14. A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is

13. Velocity of a body on reaching the point, from which it was projected upwards, is

15. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (g = 10 m/s²)

16. A ball is dropped from the top of a building 100 m high. At the same instant another ball is thrown upwards with a velocity of 40 m/s from the bottom of the building. The two balls will meet after

17. A rocket is fired vertically from the ground with a resultant vertical acceleration of 10 ms^- 2. The fuel is finished in 1 min and it continues to move up. What is the maximum height reached?

18. If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

19. Angle between two vectors of magnitudes 12 and 18 units, when their resultant is 24 units, is

20. A boat is sent across a river with a velocity of 3kmh-¹. If the resultant velocity of boat is 10 kmh-¹, then velocity of river is

21.

22. The angle between the two vectors

23. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

24. A car runs at a constant speed of a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

25. The resultant A^→ × 0 will be equal to

26. A particle starting from the origin (0, 0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are (√3,3). The path of the particle makes with the x-axis an angle of

27. A particle has initial velocity (2^i+3^j) and acceleration (0.3^i +0.2^j). The magnitude of velocity after 10 seconds will be

28. A particle has initial velocity (3^i +4^j) and has acceleration (0.4^i +0.3^j). Its speed after 10 s is

29. A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

30. The velocity of a particle moving in the x-y plane is given by

dx /dt =8πsin2πt and dy/dt = 5πcos2πt  where, t=0, x=8 and y=0, the path of the particle is

31. A body A is dropped vertically from the top of a tower. If another identical body B is thrown

horizontally from the same point at the same instant, then

32. Which of the following is constant in a projectile motion?

33. Two projectiles of same mass and with same velocity are thrown at an angle 60° and 30° with the horizontal, then which will remain same

34. If a body A of mass M is thrown with velocity v at an angle 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of horizontal range of A to B will be

35. The direction of the angular velocity vector is along

36. A 10 N force is applied on a body to produce in it an acceleration of 1 m/s².

37. A cricketer catches a ball of mass 150 g in 0.1 s moving with speed 20 m/s. Then he experiences a force of

38. A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground, the magnitude of the change in its momentum will be

39. A particle of mass m is moving with a uniform velocity v₁. It is given an impulse such that its velocity becomes v2. The impulse is equal to

40. A gun fires a bullet of mass 50 g with a velocity of 30 ms^- 1. Because of this, the gun is pushed back with a velocity of 1 ms^-¹. The mass of the gun is

41. A f0rce F^→ = (5^i+3^j+2^k)N is applied over a particle which displaces it from its origin to the point r^→ = (2^i - ^j)m. The work done on the particle (in joule) is

42. An athlete in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated in the range

43. A particle of mass 100 g is thrown vertically upwards with a speed of 5 ms^-¹. The work done by the force of gravity during the time the particle goes up is

44. A ball whose kinetic energy is E, is projected at an angle of 45° to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

45. A particle is projected at an angle of 60° to the horizontal with a kinetic energy E. The kinetic energy at the highest point is

46. A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8×10^7 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms-^2

47. A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms^-¹. The kinetic energy of the other mass is

48. A particle is moving in a circular path of radius a under the action of an attractive potential energy

U = -k/2r^2 Its total energy is

49. A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the second body?

50. A block of mass 0.50 kg is moving with a speed of 2.00ms^-¹ on a smooth surface. It strikes another mass of 1.00 kg and then move together as a single body. The energy loss during the collision is