UPSC NDA-2

1. Which one of the following statements about the Industrial Revolution

Which one of the following statements about the Industrial Revolution is correct ?

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Thomas Savery invented astrolabe
Thomas Newcomen invented chemical dyes
James Watt's invention converted the steam engine from being a mere pump into one which would provide energy to power machines in factories
Mathew Boulton discovered the technique of refining gold of impurities
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The correct answer is C) James Watt’s invention converted the steam engine from being a mere pump into one which would provide energy to power machines in factories.
James Watt’s key improvements to the steam engine, particularly the invention of the separate condenser, significantly increased its efficiency and versatility. This made the steam engine capable of producing rotary motion and thus suitable for powering a wide range of machinery in factories, which was a crucial development during the Industrial Revolution.
A) Thomas Savery invented an early steam pump, not an astrolabe, which is an ancient astronomical instrument.
B) Thomas Newcomen also invented an early atmospheric steam engine, primarily used for pumping water out of mines. Chemical dyes were developed much later, notably by figures like William Perkin in the mid-19th century.
D) Mathew Boulton was James Watt’s business partner and a key figure in manufacturing and the application of steam power, but he is not credited with discovering gold refining techniques, which predate him by centuries.
Statement C accurately describes the transformative impact of James Watt’s work on the steam engine’s role in industrial production.

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2. Starting from rest a vehicle accelerates at the rate of 2 m/s 2 towar

Starting from rest a vehicle accelerates at the rate of 2 m/s2 towards east for 10 s. It then stops suddenly. It then accelerates again at a rate of 4 m/s2 for next 10 s towards south and then again comes to rest. The net displacement of the vehicle from the starting point is

100 m
200 m
300 m
400 m
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The correct answer is C) 300 m.
The problem describes two phases of motion in perpendicular directions (East and South). The net displacement is the vector sum of the displacements in each phase. Since the displacements are perpendicular, the magnitude of the net displacement can be found using the Pythagorean theorem.
Phase 1 (towards East):
Initial velocity (u₁) = 0 m/s
Acceleration (a₁) = 2 m/s²
Time (t₁) = 10 s
Displacement in Phase 1 (s₁) = u₁t₁ + (1/2)a₁t₁² = 0*10 + (1/2)*2*(10)² = 100 m East. The vehicle stops suddenly after this displacement.

Phase 2 (towards South):
Starts from rest again, so initial velocity (u₂) = 0 m/s
Acceleration (a₂) = 4√2 m/s²
Time (t₂) = 10 s
Displacement in Phase 2 (s₂) = u₂t₂ + (1/2)a₂t₂² = 0*10 + (1/2)*(4√2)*(10)² = (1/2)*4√2*100 = 2√2*100 = 200√2 m South.

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The net displacement is the vector sum of s₁ (100 m East) and s₂ (200√2 m South). These two displacements are perpendicular.
The magnitude of the net displacement (s_net) is found using the Pythagorean theorem:
s_net² = s₁² + s₂²
s_net² = (100)² + (200√2)²
s_net² = 10000 + (40000 * 2)
s_net² = 10000 + 80000
s_net² = 90000
s_net = sqrt(90000) = 300 m.
The direction of the net displacement would be South-East, but only the magnitude is asked.

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3. There is a ball of mass 320 g. It has 625 J potential energy when rele

There is a ball of mass 320 g. It has 625 J potential energy when released freely from a height. The speed with which it will hit the ground is

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62·5 m/s
2·0 m/s
50 m/s
40 m/s
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The correct answer is A) 62·5 m/s.
When the ball is released freely from a height, its potential energy is converted into kinetic energy as it falls. By the principle of conservation of mechanical energy (assuming no air resistance), the potential energy at the initial height is equal to the kinetic energy just before hitting the ground.
The mass of the ball is m = 320 g = 0.320 kg.
The potential energy at the initial height is PE = 625 J.
Assuming the ball starts from rest, its initial kinetic energy is 0. When it hits the ground, its potential energy becomes 0 (taking the ground as the reference level).
By conservation of energy, Initial Total Energy = Final Total Energy.
PE_initial + KE_initial = PE_final + KE_final
625 J + 0 J = 0 J + KE_final
So, KE_final = 625 J.
The kinetic energy is given by KE = (1/2) * m * v², where v is the speed.
625 = (1/2) * 0.320 * v²
625 = 0.160 * v²
v² = 625 / 0.160 = 625000 / 160 = 62500 / 16
v = sqrt(62500 / 16) = sqrt(62500) / sqrt(16) = 250 / 4 = 125 / 2 = 62.5 m/s.

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4. A car weighs 1000 kg. It is moving with a uniform velocity of 72 km/h

A car weighs 1000 kg. It is moving with a uniform velocity of 72 km/h towards a straight road. The driver suddenly presses the brakes. The car stops in 0·2 s. The retarding force applied on the car to stop it is

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100 N
1000 N
10 kN
100 kN
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The correct answer is D) 100 kN.
To find the retarding force, we first need to calculate the acceleration using kinematic equations and then apply Newton’s Second Law (F=ma). The initial velocity must be converted from km/h to m/s.
The mass of the car is m = 1000 kg.
The initial velocity is u = 72 km/h. To convert to m/s, multiply by 5/18: u = 72 * (5/18) m/s = 4 * 5 m/s = 20 m/s.
The final velocity is v = 0 m/s (since the car stops).
The time taken is t = 0.2 s.
Using the kinematic equation v = u + at, we find the acceleration (a):
0 = 20 + a * 0.2
a * 0.2 = -20
a = -20 / 0.2 = -100 m/s². The negative sign indicates retardation.
The retarding force is given by F = ma:
F = 1000 kg * (-100 m/s²) = -100,000 N.
The magnitude of the retarding force is 100,000 N.
Since 1 kN = 1000 N, 100,000 N = 100 kN.

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5. The masses of two planets are in the ratio of 1 : 7. The ratio between

The masses of two planets are in the ratio of 1 : 7. The ratio between their diameters is 2 : 1. The ratio of forces which they exert on each other is

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1 : 7
7 : 1
1 : 1
2 : 1
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The correct answer is C) 1 : 1.
According to Newton’s Third Law of Motion and Newton’s Law of Universal Gravitation, the force exerted by the first planet on the second planet is equal in magnitude to the force exerted by the second planet on the first planet. This holds true regardless of the masses or distances of the objects involved in the gravitational interaction.
The force of gravity between two objects with masses m₁ and m₂ separated by a distance r is given by the formula F = G * (m₁ * m₂) / r². The force exerted by planet 1 on planet 2 (F₁₂) is equal to G * (m₁ * m₂) / r², and the force exerted by planet 2 on planet 1 (F₂₁) is also equal to G * (m₂ * m₁) / r². Therefore, F₁₂ = F₂₁, and the ratio of the forces they exert on each other is always 1:1. The information about the ratio of masses and diameters is extraneous to the question about the ratio of forces *between* them.

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6. Which one of the following statements best defines the concept of heat

Which one of the following statements best defines the concept of heat ?

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The transformation of energy from one form to another
The conversion of energy into mass and vice-versa due to temperature difference
The transfer of energy due to temperature difference
The change in volume of a substance with temperature
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Heat is defined as the transfer of thermal energy between systems or objects of different temperatures. Energy naturally flows from a region of higher temperature to a region of lower temperature.
Heat is energy in transit, whereas temperature is a measure of the average kinetic energy of the particles within a substance. When there is a temperature difference between two objects or systems in thermal contact, energy is transferred between them, and this transferred energy is called heat.
The other options describe related concepts but not the definition of heat itself. Option A describes energy transformation (e.g., chemical to thermal). Option B relates to mass-energy equivalence and is not the definition of heat. Option D describes thermal expansion, which is a consequence of temperature change, not the definition of heat transfer.

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7. An incandescent electric bulb converts 20% of its power consumption in

An incandescent electric bulb converts 20% of its power consumption into light, and the remaining power is dissipated as heat. The bulb’s filament has a resistance of 200 Ω and 2 A current flows through it. If the bulb remains ON for 10 h and the rate of electricity charge is ₹5/unit, then which among the following is the correct amount for the money spent on producing light ?

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₹5
₹6
₹7
₹8
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The power consumed by the incandescent bulb is calculated using the given resistance and current. The total energy consumed over 10 hours is then calculated. Since only 20% of the power (and thus energy) is converted into light, the energy spent on producing light is 20% of the total energy consumed. The cost is calculated based on the rate per unit (kWh) for this amount of energy.
Power consumed (P) = I²R = (2 A)² * 200 Ω = 4 * 200 = 800 W = 0.8 kW.
Total energy consumed (E_total) = Power * Time = 0.8 kW * 10 h = 8 kWh.
Total cost of electricity = E_total * Rate = 8 kWh * ₹5/kWh = ₹40.
Energy converted into light (E_light) = 20% of E_total = 0.20 * 8 kWh = 1.6 kWh.
Cost spent on producing light = E_light * Rate = 1.6 kWh * ₹5/kWh = ₹8.
Incandescent bulbs are inefficient in converting electrical energy into visible light; a large portion of the energy is dissipated as heat, which is why the question specifies that only 20% is converted to light. The remaining 80% (1.6 kWh * 4 = 6.4 kWh) is dissipated as heat, costing ₹32 (₹40 – ₹8).

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8. A pumpkin weighs 7.5 N. On submerging it completely in water, ¾ L of w

A pumpkin weighs 7.5 N. On submerging it completely in water, ¾ L of water gets displaced. The acceleration due to gravity at the place where the pumpkin was weighed is 10 m/s². Which one of the following is the correct value of the density of the pumpkin ?

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10 kg/m³
100 kg/m³
1000 kg/m³
10000 kg/m³
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The weight of the pumpkin is given as 7.5 N. Using the formula Weight = mass × gravity, the mass of the pumpkin can be calculated. When the pumpkin is completely submerged, the volume of water displaced is equal to the volume of the pumpkin. Given the volume of displaced water, we can calculate the volume of the pumpkin. Density is then calculated as mass divided by volume.
Mass of pumpkin (m) = Weight / gravity = 7.5 N / 10 m/s² = 0.75 kg.
Volume of water displaced (V_displaced) = 3/4 L = 0.75 L.
Converting litres to cubic meters: 1 L = 0.001 m³. So, V_displaced = 0.75 × 0.001 m³ = 0.00075 m³.
When completely submerged, Volume of pumpkin (V_pumpkin) = V_displaced = 0.00075 m³.
Density of pumpkin (ρ) = Mass / Volume = 0.75 kg / 0.00075 m³.
ρ = 0.75 / (7.5 × 10⁻⁴) = (7.5 × 10⁻¹) / (7.5 × 10⁻⁴) = 10³ kg/m³ = 1000 kg/m³.
The density of water is approximately 1000 kg/m³. A pumpkin with a density equal to or slightly less than water would float or remain suspended when fully submerged. The fact that it displaces ¾ L of water upon complete submersion means its volume is ¾ L. The calculation of density confirms it is very close to the density of water, which is reasonable for a pumpkin.

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9. A vehicle starts moving along a straight line path from rest. In first

A vehicle starts moving along a straight line path from rest. In first `t` seconds it moves with an acceleration of 2 m/s² and then in next 10 seconds it moves with an acceleration of 5 m/s². The total distance travelled by the vehicle is 550 m. The value of time `t` is

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10 s
13 s
20 s
25 s
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The motion consists of two phases of constant acceleration. We need to find the time ‘t’ in the first phase such that the total distance covered in both phases is 550 m. By calculating the distance in each phase and setting the total distance equal to 550 m, we arrive at a quadratic equation in ‘t’. Solving this equation gives t = 10 s (the positive solution).
For the first phase (0 to t seconds): Initial velocity (u₁) = 0, acceleration (a₁) = 2 m/s². Distance s₁ = u₁t + (1/2)a₁t² = 0*t + (1/2)*2*t² = t². Velocity at time t (v₁) = u₁ + a₁t = 0 + 2t = 2t m/s.
For the second phase (t to t+10 seconds): Initial velocity (u₂) = v₁ = 2t m/s, acceleration (a₂) = 5 m/s², time (t₂) = 10 s. Distance s₂ = u₂t₂ + (1/2)a₂t₂² = (2t)*10 + (1/2)*5*(10)² = 20t + 250 m.
Total distance = s₁ + s₂ = t² + 20t + 250. Given total distance is 550 m, t² + 20t + 250 = 550, which simplifies to t² + 20t – 300 = 0.
Factoring the quadratic: (t + 30)(t – 10) = 0. Possible solutions are t = -30 or t = 10. Since time cannot be negative, t = 10 s.
We can verify the answer: If t=10 s, s₁ = 10² = 100 m. Velocity after 10s is v₁ = 2*10 = 20 m/s. In the next 10s, starting at 20 m/s with acceleration 5 m/s², distance s₂ = 20*10 + (1/2)*5*10² = 200 + 250 = 450 m. Total distance = s₁ + s₂ = 100 + 450 = 550 m, which matches the given information.

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10. Which one among the following is correct for a person suffering from m

Which one among the following is correct for a person suffering from myopia ?

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The person can see near objects clearly
The person can see distant objects clearly
The person cannot distinguish colours
The person can neither see near objects nor distant objects clearly
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Myopia, or nearsightedness, is a common refractive error where light focuses in front of the retina instead of on it. This results in distant objects appearing blurred, while near objects can be seen clearly.
A person with myopia has difficulty seeing objects that are far away. The eye might be longer than normal, or the cornea might be too curved, causing light to converge too strongly.
Myopia can be corrected using diverging lenses (concave lenses), which cause the light rays to diverge slightly before entering the eye, thereby shifting the focal point back onto the retina. Hyperopia (farsightedness) is the opposite condition, where near objects are blurred. Astigmatism causes blurred vision at all distances due to an irregularly shaped cornea or lens.

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