19 reviewed questions with answers and explanations.
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Question 1
Simple pendulums P,Q,R,S,T andU hang from a common support. T has the same length asP; R is shorter, while Q,S andU are longer. Which resonates withP whenP oscillates with small amplitude?
- T
- U
- R and T
- Q and R
Answer and explanation
A: T
For small oscillations, a simple pendulum’s natural period depends on its length, T =2π√(L/g). T has the same length asP, so it has the same natural frequency and resonates withP.
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Question 5
A metal sphere of radius 3 cm is fully immersed in water in a vertical cylindrical vessel without overflow. The water level rises 1 cm. Find the vessel’s internal radius.
- 12 cm
- 1 cm
- 3 cm
- 6 cm
Answer and explanation
D: 6 cm
The displaced volume equals the sphere volume:πR² ×1 =(4/3)π ×3³. Cancellingπ gives R² =36, hence the cylinder radius is 6 cm.
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Question 8
For a real machine with energy losses and efficiency below 100%, which relationship holds?
- Work output exceeds work input
- Load always exceeds effort
- Effort always exceeds load
- Velocity ratio exceeds mechanical advantage
Answer and explanation
D: Velocity ratio exceeds mechanical advantage
For a machine, efficiency =MA/VR. Energy losses make efficiency less than one, so mechanical advantage MA must be less than velocity ratio VR.
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Question 10
Ice cubes are added to warm water in a glass. Which pair of heat-transfer mechanisms mainly cools the water and glass?
- Conduction only
- Convection only
- Conduction and convection
- Convection and radiation
Answer and explanation
C: Conduction and convection
Heat reaches the ice by conduction at contacting surfaces and by convection as water circulates and carries thermal energy. Conduction through the glass also helps it cool toward the water temperature.
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Question 13
Compared with a simple astronomical refracting telescope, a traditional terrestrial telescope includes an extra erecting lens mainly for
- Improving the sharpness
- Creating an inverted image
- Magnification of the image
- Erection of the image
Answer and explanation
D: Erection of the image
A simple astronomical telescope gives an inverted view. The extra erecting lens in a traditional terrestrial telescope inverts that intermediate image again, producing an upright view.
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Question 14
A convex car mirror has radius of curvature 1 m. A vehicle is 4 m in front of it. Using the paraxial mirror formula, find the image distance behind the mirror.
- 8/7 m
- 4/9 m
- 9/2 m
- 4/7 m
Answer and explanation
B: 4/9 m
A convex mirror has focal length−R/2 =−0.5 m. From 1/f =1/u +1/v with u =4 m,1/v =−2 −1/4 =−9/4, so v =−4/9 m: the image is 4/9 m behind the mirror.
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Question 15
A ray enters a transparent medium from air. Its incident ray makes angleα with the surface, while its refracted ray makes angleβ with the normal. Taking air’s refractive index as 1, find the medium’s refractive index.
- cosα/sinβ
- sinα/sinβ
- cosβ/sinα
- sinβ/sinα
Answer and explanation
A: cosα/sinβ
The incident angle from the normal is 90° −α, becauseα is measured from the surface. Snell’s law for air gives n =sin(90° −α)/sinβ =cosα/sinβ.
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Question 20
Which listed substance is used as the gas in primary gas thermometry to determine thermodynamic temperature?
- Alcohol
- Mercury
- Helium
- Platinum
Answer and explanation
C: Helium
Helium gas is used in primary gas thermometry because its pressure, volume or sound speed can be related to thermodynamic temperature. It remains gaseous over a wide range and can be studied in the dilute-gas limit.
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Question 22
A 6 V d.c. supply drives 3 Ω and 1 Ω resistors in series with a parallel pair of 10 Ω and 5 Ω resistors. Find the total currentI before it splits between the parallel branches.
- 3/8 A
- 9/11 A
- 11/9 A
- 8/3 A
Answer and explanation
B: 9/11 A
The 10 Ω and 5 Ω branches have equivalent resistance 10/3 Ω. In series with 3 Ω and 1 Ω, the total is 22/3 Ω. Thus I =6/(22/3) =9/11 A.
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Question 23
Capacitors P =2 μF and Q =4 μF are connected in parallel across the same d.c. voltage. Find the ratio of energy stored inP to that inQ.
- 4 : 1
- 2 : 1
- 1 : 4
- 1 : 2
Answer and explanation
D: 1 : 2
Both parallel capacitors have the same voltage. Since energy is½CV², their energy ratio is C_P/C_Q =2/4 =1/2, or 1:2.
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Question 25
Initially uncharged capacitors C₁ =2 μF,C₂ =6 μF andC₃ =3 μF are connected in one series chain across 12 V. Find their final voltages in that order.
- 4 V, 6 V and 2 V
- 2 V, 6 V and 4 V
- 6 V, 4 V and 2 V
- 6 V, 2 V and 4 V
Answer and explanation
D: 6 V, 2 V and 4 V
In an initially uncharged series chain, all three capacitors acquire equal charge. The equivalent capacitance is 1 μF, giving charge 12 μC. Their voltages are 12/2 =6 V,12/6 =2 V and 12/3 =4 V.
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Question 29
In a Daniell cell, the depolarizing solution, positive electrode and negative electrode are respectively
- Copper sulfate, copper and zinc
- Manganese dioxide, carbon and zinc
- Sulfuric acid, lead dioxide and lead
- Potassium hydroxide, nickel and iron
Answer and explanation
A: Copper sulfate, copper and zinc
In a Daniell cell, zinc is oxidized at the negative electrode and copper ions are reduced at the positive copper electrode. Copper sulfate supplies those ions and is traditionally described as the depolarizer.
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Question 30
A closed cube of side 0.5 m lies in a uniform electric fieldE parallel to one pair of opposite-face normals. Find its net outward electric flux.
- 0.5 E
- 2.0 E
- 0.2 E
- 0.0 E
Answer and explanation
D: 0.0 E
For a uniform electric field, equal flux enters and leaves opposite faces of a closed cube. The signed contributions cancel, while the other faces have zero normal component. Net outward flux is zero.
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Question 33
A glass dielectric block is inserted into the air gap of a parallel-plate capacitor without changing plate area or separation. Its capacitance will
- Increase
- Decrease
- Decrease, then increase
- Remain constant
Answer and explanation
A: Increase
Glass polarizes in the electric field. For a given plate charge this reduces the potential difference, so C =Q/V increases when glass replaces air between plates at unchanged geometry.
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Question 34
Two protons in vacuum, each with charge e and mass m, are separated by distance d. Find the ratio of electric-force magnitude to gravitational-force magnitude.
- e/(4πε₀Gm)
- e²/(Gm²)
- Gm²/(4πε₀e²)
- e²/(4πε₀Gm²)
Answer and explanation
D: e²/(4πε₀Gm²)
The electric force magnitude is e²/(4πε₀d²), while gravity gives Gm²/d². Dividing cancels d², leaving F_E/F_G =e²/(4πε₀Gm²).
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Question 38
A 240 V RMS sinusoidal supply is connected across a 4 Ω resistor in series with an ideal inductor of reactance 3 Ω. Find the RMS current.
- 31 A
- 48 A
- 60 A
- 80 A
Answer and explanation
B: 48 A
The series resistance is 4 Ω and inductive reactance 3 Ω, so impedance magnitude is √(4² +3²) =5 Ω. The RMS current is 240/5 =48 A.
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Question 40
Current through a resistor is i =2 sin(ωt) A. Find the steady d.c. current that would produce the same average heating.
- 1/√2 A
- 2√2 A
- 2 A
- √2 A
Answer and explanation
D: √2 A
The d.c. heating equivalent is the RMS current. For i =2 sin(ωt) A, the peak is 2 A, so I_RMS =2/√2 =√2 A.
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Question 44
The process of energy production in the sun is
- Nuclear fission
- Nuclear fusion
- Electron collision
- Radioactive decay
Answer and explanation
B: Nuclear fusion
The Sun’s core releases energy mainly by nuclear fusion, combining hydrogen nuclei into helium. The products have slightly less total rest mass, with the difference released as energy.
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Question 46
For fixed current, length and uniform magnetic-field strength, the magnetic force on a straight conductor is greatest when it is
- At 60° to the field
- At any angle, since force is angle-independent
- Parallel to the field
- At right angles to the field
Answer and explanation
D: At right angles to the field
For a straight conductor in a uniform magnetic field, F =BIL sinθ. With B,I andL fixed, the force is largest at θ =90°, where sinθ =1.
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