31. Two objects P and Q of masses 100kg and 20kg respectively are 1.2m apart on a horizontal surface. Calculate the net gravitational force acting on Q. \([G= 6.67 \times 10^{-11} Nm^{2}kg^{-2}]\)
- A. \(1.11\times 10^{-7} N\) towards P
- B. \(1.11\times 10^{-7} N\) towards Q
- C. \(9.26\times 10^{-8} N\) towards P
- D. \(9.26\times 10^{-8} N\) towards Q
Correct Option: Answer is D
\(F= \frac{Gm_{1}m_{2}}{r^{2}}\) \(m_{1} = 100kg\) \(m_{2} = 20kg; r =1.2m\) \(G= 6.67\times 10^{-11}\) \(F = \frac{6.67\times 10^{-11}\times 100\times 20}{(1.2)^{2}} = 9.26\times 10^{-8}\) The acceleration of each object is inversely proportional to the mass, the lighter object will move a bit faster, hence. the force will act in the direction of Q.32. The primary of a transformer has 100 turns and its secondary has 200 turns. If the voltage at the primary is 100V, determine the voltage at the secondary.
- A. 50V
- B. 100V
- C. 200V
- D. 400V
Correct Option: Answer is C
The ideal transformer (either step-up or step-down) works with the equation:
\(\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}} = \frac{I_{p}}{I_{s}}\)
where \(V_{s}\) and \(V_{p}\) are the voltages applied to the secondary and the primary respectively
\(N_{s}\) and \(N_{p}\) are the number of turns on the secondary and primary coils respectively
\(I_{p}\) and \(I_{s}\) are the currents flowing in the primary and secondary coils respectively.
\(\frac{V_{s}}{100} = \frac{200}{100}\)
\(V_{s} = \frac{200\times 100}{100} = 200V\)
33. In the diagram illustrated a block of mass M is at rest on a plane inclined at an angle to the horizontal. As θ increases, the velocity ratio of the plane
- A. increases
- B. decreases
- C. remain the same
- D. decreases and later increases
Correct Option: Answer is B
The velocity ratio and therefore, the mechanical advantage of an inclined plane system increases as θ decreases and vice-versa.
34. When the speed of a car is halved, its kinetic energy is
- A. doubled
- B. quartered
- C. halved
- D. quadrupled
Correct Option: Answer is B
p>Given \(K_{1}\) = \(\frac{mv^{2}}{2}\).
When v is halved, we have
\(K_{2}\) = \(\frac{m\times (\frac{v}{2})^{2}}{2}\)
= \(\frac{K_{1}}{4}\)
Hence, the initial kinetic energy is quartered.
35. A wire of length 400cm is stretched between two fixed points. When plucked, its fundamental frequency is 150Hz. Calculate the speed of the wave produced.
- A. 250ms−1
- B. 625ms−1
- C. 1200ms−1
- D. 1500ms−1
Correct Option: Answer is C
The fundamental frequency \((f_{0})\) = \(\frac{v}{2l}\)
\(f_{0} = 150Hz; l =400cm = 4m\)
\(150 = \frac{v}{2\times 4}\)
\(v = 150 \times 8 = 1200ms^{-1}\)
36.
The diagram above illustrates a waveform. Determine the number of wavelengths in it
- A. 4
- B. 3 1/2
- C. 2 1/2
- D. 2
Correct Option: Answer is C
37. A resistor with fixed resistance value is called a
- A. resistance box
- B. standard resistor
- C. shunt resistor
- D. multiplier resistor
Correct Option: Answer is B
38. Which of the following statements is not an advantage of an alkaline accumulator?
- A. The electrolyte does not need attention
- B. It can be recharged
- C. It has low internal resistance
- D. It has a much longer life than lead-acid accumulator
Correct Option: Answer is A
39. The diagram above illustrates the wire connections to a three-pin plug. The wires P, Q and R respectively are:
- A. live, neutral and earth
- B. neutral, earth and live
- C. earth, live and neutral
- D. earth, neutral and live
Correct Option: Answer is B
40. Which of the following statements about parallel plate capacitors is/are correct?
I. Capacitance of the capacitor is inversely proportional to the distance between the plates
II. Capacitors can filter a.c signals from d.c
III. Capacitors can store charges
- A. I only
- B. I and II only
- C. II and III only
- D. I, II and III