Sand falls vertically on a conveyor belt at a rate of 0.1 kg/s. In order to keep the belt moving at a uniform speed of 2 m/s, the force required to be applied on the belt is :
- A.0 N
- B.0.2 N
- C.1.0 N
- D.2.0 N
Correct answer
Explanation
The correct answer is B, 0.2 N. The force needed equals the rate at which the belt must give horizontal momentum to the falling sand: F = v × (dm/dt) = 2 × 0.1 = 0.2 N.
Newton's second law, in its general form, says force equals the rate of change of momentum. The sand lands with no horizontal speed, and the belt must speed every kilogram up to 2 m/s. Each second 0.1 kg of sand arrives, so each second the belt must supply 0.1 × 2 = 0.2 kg m/s of new momentum. A steady force of 0.2 N does exactly that, so the belt keeps a uniform speed even though its load keeps growing.
A is wrong because without a force the added sand would slow the belt down. C is wrong because 1.0 N would supply five times the momentum needed and the belt would speed up. D is wrong because 2.0 N is ten times the needed force.
Exam tip: when mass is added at a steady rate, F = v × dm/dt, the same idea as rocket thrust.
Practice Questions
View allWhich of the following statements about electromagnetic waves, sound waves and water waves is/are correct ? 1. They exhibit reflection 2. They carry energy 3. They exert pressure 4. They can travel in vacuum Select the correct answer using the code given below :
- A.1,2 and 3
- B.2 and 4
- C.1 and 3 only
- D.1 only
Show answer
All three kinds of wave reflect, carry energy and exert pressure, but only electromagnetic waves can travel through a vacuum.
Read the full explanation →Which one of the following is NOT the unit of energy?
- A.Joule
- B.Watt-hr
- C.Newton-metre
- D.kg-metre/sec²
Show answer
A kilogram-metre per second squared is mass times acceleration, which is force; it is the newton, not a unit of energy.
Read the full explanation →To protect steel and iron from rusting, a thin layer of which one of the following metals is applied?
- A.Magnesium
- B.Zinc
- C.Aluminium
- D.Lead
Show answer
Coating iron or steel with a thin layer of zinc is called galvanisation, and it is the most common way to protect them from rusting.
Read the full explanation →In an electric circuit, a wire of resistance 10 Ω is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
- A.half of its original value.
- B.double of its original value.
- C.one-fourth of its original value.
- D.four times of its original value.
Show answer
Stretching the wire to twice its length makes its resistance four times larger, so at the same voltage the current falls to a quarter.
Read the full explanation →Which one of the following scientists mentioned that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy ?
- A.Ernest Rutherford
- B.J.J. Thomson
- C.Niels Bohr
- D.Albert Einstein
Show answer
In his 1913 model of the atom, Bohr proposed that electrons move in certain fixed orbits, called stationary states, in which they do not radiate energy.
Read the full explanation →