For a particle in uniform circular motion (radius R and angular velocity ω), the magnitude and direction of acceleration, respectively are
- A.ωR, along the radius outward
- B.ωR, towards the centre of the circle
- C.ω²R, towards the centre of the circle
- D.ω²R, along the linear velocity
Correct answer
Explanation
The correct answer is C, ω²R, towards the centre of the circle. In uniform circular motion the speed stays the same but the direction keeps turning, and that change needs an acceleration pointing to the centre.
This is the centripetal acceleration. With linear speed v = ωR, its size is a = v²/R = ω²R. It always points along the radius towards the centre, at right angles to the velocity, so it changes the direction of motion without changing the speed. The force that supplies it is the centripetal force mv²/R, such as the tension in a string whirling a stone or gravity holding a satellite in orbit.
A is wrong because ωR is the linear speed, not the acceleration, and the acceleration points inward. B is wrong because, although the direction is right, ωR has the units of speed. D is wrong because an acceleration along the velocity would change the speed, which stays constant here.
Exam tip: v = ωR; centripetal a = v²/R = ω²R, always towards the centre.
Practice Questions
View allWhich one of the following is not used as fertilizer?
- A.Ammonium nitrate
- B.Ammonium sulphide
- C.Ammonium phosphate
- D.Ammonium sulphate
Show answer
Ammonium sulphide is an unstable, foul-smelling compound that breaks down to release ammonia and toxic hydrogen sulphide, so it is not used as a fertiliser.
Read the full explanation →The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is
- A.12.5 cm
- B.5 cm
- C.2 cm
- D.10 cm
Show answer
For an astronomical telescope in normal adjustment the magnifying power equals the focal length of the objective divided by that of the eyepiece, so the eyepiece focal length is 50 ÷ 25 = 2 cm.
Read the full explanation →The major source of vitamins and minerals for vegetarians is
- A.black gram and wheat.
- B.rice and mustard.
- C.vegetables and fruits.
- D.soya bean and milk.
Show answer
Vegetables and fruits supply most of the vitamins and minerals in a vegetarian diet, which is why they are called protective foods.
Read the full explanation →Which one of the following compounds is used in black and white photography?
- A.AgF
- B.AgBr
- C.AgCl
- D.Ag2SO4
Show answer
Silver bromide is the light-sensitive compound coated on black and white photographic film and paper, because light breaks it down into tiny grains of silver metal.
Read the full explanation →Which one of the following statements about speed and velocity is correct?
- A.Speed and velocity both are vector quantities.
- B.Speed and velocity both are scalar quantities.
- C.Speed is vector quantity and velocity is scalar quantity.
- D.Speed is scalar quantity and velocity is vector quantity.
Show answer
Speed tells only how fast a body moves, while velocity also tells the direction of motion, and a quantity with both magnitude and direction is a vector.
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