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.

(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not a correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

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?

(a) 12 cm
(b) 10 cm
(c) 8 cm
(d) 6 cm

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.

(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not a correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

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: g_{r} = g_{o} * ((re)/(r_{e} + h)) ^ 2

Where

g, is the gravity measure at height above sea level.

r is the Earth's mean radius.

g, is the standard gravity.

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?

(a) 1 and 3
(b) 2 and 4
(c) 2 and 3
(d) 1 and 4

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.

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

(a) remains horizontal.
(b) is inclined to the horizontal with smaller depth at the rear end.
(c) is inclined to the horizontal with larger depth at the rear end.
(d) assumes a parabolic curve.

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.

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]

(a) increase by 0.5%
(b) increase by 2%
(c) decrease by 0.5%
(d) decrease by 2%

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]

(a) driving force in the direction of car's motion
(b) resistance force opposite to the direction of car's motion
(c) an inclined force
(d) equal to zero

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.

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]

(a) The body has no acceleration
(b) The body has a radial acceleration w2r directed toward centre of path
(c) The body has a radial acceleration 2/5w2r directed away from the centre of the path
(d) The body has an acceleration 62 tangential to its path

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]

(a) 9.8/5 N
(b) 9.8/10 N
(c) 9.8/2 N
(d) zero

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]

(a) Steel > Mercury > Gold
(b) Gold > Mercury > Steel
(c) Steel > Gold > Mercury
(d) Gold > Steel > Mercury

Correct Answer: (b) Gold > Mercury > Steel

Solution:Density of gold is 19.3g / c * m³ The density of ultra pure liquid mercury is 13.534g / c * m³ and the density of steel is 7.80 g / c * m³

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