MTH 104 CBT PRACTICE TEST

1. Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.

2. A car is moving at 120kmh−1. Find its speed in ms−1.

3. Let the position of a particle P be given at time t seconds by r(t) = 2t i  + (t² -1) j + 3k , find the displacement of P at the end of 2 seconds?

4.

Which of the following is a fundamental quantity?

5. The position vector of a particle is given at time t by r(t) = 2t i – 3t² j , calculate the velocity of the particle

6. A body moves with varied acceleration a =6t – 4 and at a time t=0 the body is moving with velocity 3m/s and has a displacement 5m from the origin. Find in terms of t expression for the velocity of the particle

7. The speed of a car increases from 10m/s to 15m/s and its kinetic energy increases by E₁ later the speed of the car increases from 15m/s to 25m/s and its kinetic energy increase by E₂. What is the ratio E₁/E₂? By

8. A particle starts from rest and moves through a distance S=12t2−2t3 metres in time t seconds. Find its acceleration in 1 second.

9. What is the radius of gyration of a circular plate of diameter 26cm?

10. What is the dimension of Tension

11. Copy - A particle starts from rest and moves through a distance S=12t2−2t3 metres in time t seconds. Find its acceleration in 1 second.

12. The path of a particle is given by r(t) = (t²-t)I + (t² +t)j, the particle is at (0,2,0) when t is?

13. A ball is thrown vertically upward on the moon returns to its starting point in 4.0s. The acceleration due to gravity there is 1.6m/s² downward. Find the ball’s original speed

14. A man of mass 70kg climbs a ladder to the top of  15m height. Calculate the workdone by the weight.

15. A car drive for 2h at 40km/h , then for another 2h at 60km/h. What is the car average speed?

16. A wheel is rotating at 180rpm. Find its moment of inertia if its mass is 10Kg and radius of gyration is 25cm

17. A runner covers one lap of a circular track 40.0m in diameter in 62.55 secs. For that lap, what were her average speed and average velocity?

18. An experiment to measure the force of gravity is set up using two large spheres. The spheres are both 100kg and their mass are 2m apart. What is the force of gravity between these two spheres

19. A stone which is thrown vertically upward with an initial speed of 80m/s is acted upon by an acceleration called gravity 10ms in the downward direction. Find the maximum height above the point of projection which is attained by the stone

20. A stone of mass 0.1Kg is skimmed across ice. It starts at 5m/s and across to rest after 50m, Find the coefficient of friction

21. Copy - A boat initially at rest moving at 20m/s is only moving at 2 m/s in the same direction, 25 seconds later. Assuming that the boat’s acceleration was constant, what was the boat's acceleration during this time?

22. Copy - The speed of a car increases from 10m/s to 15m/s and its kinetic energy increases by E₁ later the speed of the car increases from 15m/s to 25m/s and its kinetic energy increase by E₂. What is the ratio E₁/E₂? By

23. Given a particle moves from point 0 with velocity v = 3t² -6t +3 and that when t=1, and s=2m find the expression for the acceleration of the particle

24. If a 150g ball is tied to a pole with a rope of length 1.5m and it spins around the pole at 30m/s. what is the centripetal force?

25. A crate of mass 100kg is sliding down the slope that is at an angle of 30^o. A frictional force of 90N acts on the slope , calculate the net force acting on the incline

26. A body of mass 12kg hangs from a string and is pulled aside by horizontal force of 30N. Find the tension in the string

27. A boat initially at rest moving at 20m/s is only moving at 2 m/s in the same direction, 25 seconds later. Assuming that the boat’s acceleration was constant, what was the boat's acceleration during this time?

28. A body travelling with a speed of 10m/s has kinetic energy 1500J. If  the speed of the body is increased to 40ms^-1, what is its new kinetic energy?

29. Calculate excess pressure in an air bubble of radius 6mm. Surface tension of liquid is 0.58N/m

30. The position vector of a particle is give at time t by r(t) = 2t i  + (t² -1) j + 3k

Find the position vector at t= 2