Physics (Part-I) (UPSC)

Total Questions: 50

21. The following two items consist of two statements, one labeled as the Assertion (A) and the other as Reason (R). You have to answer these items using the code given below. [2002]

Assertion (A): An iron ball floats on mercury but gets immersed in water.
Reason (R): The specific gravity of iron is more than that of mercury.

Correct Answer: (c) A is true but R is false
Solution:

Statement 1 is true but statement 2 is false. Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance. Mercury has a specific gravity of 13.56 whereas specific gravity of iron is 7.21. Thus, iron ball floats on mercury.

22. A solid cube gets completely immersed in water when a 0.2 kg mass is placed on it. If the mass is removed, the cube is 2 cm above the water level. What is the length of each side of the cube?

Correct Answer: (b) 10 cm
Solution:

The volume of 2 cm part of the cube, assuming the side of cube is x.
Volume 2xxxx=2x²
Mass displaced by this portion = 0.2kg = 200gm Using

Mass Volume × density
200 = 2x² * 1
x² = 100
x = 10cm

23. The following item consists of two statements, one labeled as the Assertion (A) and the other as Reason (R). You have to answer this items using the code given below. [2003]

Assertion (A): The weight of a body decreases with the increase of altitude on earth.

Reason (R): The earth is not a perfect sphere.

Correct Answer: (b) Both A and R are true but R is not a correct explanation of A
Solution:Weight is basically the measurement of the gravitational force that acts on an object. Weight of any body is given by formula

W = mg

Where m is the mass of body.

g refers to the acceleration that the Earth imparts to objects on or near its surface. It is called acceleration due to gravity.

Now, mass is universal constant. It will remain same at earth surface or at any point above the surface of earth. Acceleration due to gravity decreases with altitude, since greater altitude means greater distance from the Earth's centre. The following formula approximates the Earth's gravity formula variation with altitude:

Earth is not a perfect sphere because its two poles cause it to bulge out in the middle. It spins on its axis and the centrifugal force makes the part at the equator bulge out slightly.

24. Consider the following statements: [2003]

A 4-wheel vehicle moving in a sharp circular path at high speed will:

  1. overturn about its outer wheels
  2. overturn about its inner wheels
  3. skid outwards
  4. skid inwards

Which of these statements are correct?

Correct Answer: (a) 1 and 3
Solution:In case of object moving along a circular path two types of forces centripetal and centrifugal acts upon it. As they have opposite impact thus, the object remains in balance. When centrifugal force gets disturbed then the object will leave the balance and skid toward an outward direction.
Centripetal Force: A force which acts on a body performing circular motion and acts along the radius of the circular path and directed towards the center of the path is called centripetal force. Without centripetal force, circular motion is not possible. In the case of turning vehicle centripetal force generates with the help of friction between road and the tyres.
Centrifugal Force: It is the imaginary force which acts on the particle performing circular motion in the direction away from the center along the radius of the circular path having the same magnitude as that of centripetal force. In short centrifugal force pushes the car outwards. Now we know that as the center of mass of the car is above the level of the wheels of the vehicle, and hence it tends to create a moment which will push the outer wheels in the downward direction and the inner wheels in the upward direction.

25. An oil tanker partially filled with oil moves forward on a level road with uniform acceleration. The free surface of oil then: [2003]

Correct Answer: (c) is inclined to the horizontal with larger depth at the rear end.
Solution:

The surface of tanker will move in forward direction with increasing velocity (as acceleration in uniform), so depth will be larger at the rear end.
• Inertia: The oil inside the tanker resists the change in motion (acceleration).
• Piling Up: As the tanker speeds up forward, the oil “pushes back” or lags, creating a higher surface (deeper) at the rear of the tank.
• Dipping: Simultaneously, the oil level dips at the front of the tank, where the tanker is accelerating towards.
• Angle of Inclination: The surface forms a plane tilted at an angle θ to the horizontal, where tanθ = a/g (tangent theta equals a / g; a is the tanker’s acceleration, g is gravity).

26. If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of g on the earth's surface would: [2003]

Correct Answer: (b) increase by 2%
Solution:The acceleration due to gravity on the surface of the Earth, g, is given by the formula:

g = (GM)/(R²)

where

G is the gravitational constant,

M is the mass of the Earth,

R is the radius of the Earth.

If the radius R decreases by 1%, the new radius R' is: R' = 0.99R

The new acceleration due to gravity g' will be:

g prime = GM (R)² = (GM)/(0.99R)² = (GM)/(0.9801R²)

Thus :

g' = g/0.9801 \approx 1.0204g

This shows that the acceleration due to gravity increases by approximately 2%.

27. A car is running on a road at a uniform speed of 60 km/h. The net resultant force on the car is: [2004]

Correct Answer: (d) equal to zero
Solution:By Newton's second law F = ma If a = 0 F net =0 Thus, the resultant force is zero.
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
In physics, the term ‘net force’ is used to describe the total force acting on an object after considering all the individual forces. It’s the resultant force that can accelerate a mass. When numerous forces act on a body, either at rest or in motion, the net force comes into play. The concept of net force is crucial when dealing with systems where multiple forces are in action.

28. A spherical body moves with a uniform angular velocity (0) around a circular path of radius r. Which one of the following statements is correct? [2004]

Correct Answer: (b) The body has a radial acceleration w2r directed toward centre of path
Solution:When an object moves in a circular path with a uniform angular velocity o, it experiences a centripetal (or radial) acceleration directed toward the center of the circular path. This centripetal acceleration is given by the formula.

a_{r} = omega² * r where r is the radius of the circular path. This acceleration is always directed towards the center of the circle, not tangentially or away from the center.

29. A weightless rubber balloon is filled with 200 cc of water. Its weight in water is equal to: [2004]

Correct Answer: (d) zero
Solution:In this case, balloon is filled up with water and then put into water. Initially, after some oscillations it become stable because the downward directing force exerted by weight of water in balloon is balanced by the upward directing buoyancy force of water. Hence, the resultant weight in water is zero as there is no resultant force acting upon it.

30. Which one of the following is the correct sequence of the given substances in the decreasing order of their densities? [2005]

Correct Answer: (b) Gold > Mercury > Steel
Solution:Density of gold is 19.3g / cm³ The density of ultra pure liquid mercury is 13.534g / cm³ and the density of steel is 7.80 g / cm³

The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol representing density or it can also be represented by the letter D.
Iron, platinum, and lead are examples of dense materials. Many types of rock and minerals are examples of dense material. Materials that are dense are most likely to ‘feel’ heavy or hard. The opposite of dense is sparse and a few examples of sparse material are glass, bamboo, aluminium, and styrofoam. In general, liquids are less dense than solids and gases are less dense than liquids. This is due to the fact that solids have densely packed particles, liquids are materials where particles can slide around one another, and gases have particles that are free to move all over the place.