SAT (Stage-2) Mock Test

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SAT (Stage-2) Mock Test - 34

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Weekly Quiz Competition

Question 1
1 / -0

A wire has a resistance of 1 Ω. It is stretched to double its length. The resistance of the wire will be

A
1 Ω

B
2 Ω

C
4 Ω

D
16 Ω

Solution

Here the length of the wire is doubled but the volume of the wire remains same
Question 2
1 / -0

A compass needle pointer, not under the influence of any magnet and freely suspended, points in the ______ direction.

A
south

B
east

C
north

D
west

Solution

If a compass needle pointer is not under the influence of any magnet and is freely suspended, then it points in the north direction.

Hence, option (3) is correct.
Question 3
1 / -0

A system consists of masses M and m (< M). The centre of mass of the system is

A
at the middle

B
nearer to M

C
nearer to m

D
at the position of large mass

Solution

∵ Distribution of mass is more towards M(m << M)
⇒ Centre of mass will be farther from m
⇒ r₁ > r₂
So, Centre of mass will be nearer to M.
Question 4
1 / -0

A parachutist of weight W strikes the ground with his legs fixed and comes to rest with an upward acceleration of 3g. The force exerted by him on the ground during landing is

A
W

B
2W

C
3W

D
4W

Solution

A parachutist of weight W strikes the ground with his legs fixed and comes to rest with an upward acceleration of 3g.
Let F is the upward force
ma = F - mg
m(3g) = F - mg
F = 3mg + mg = 4 mg
F = 4W
Question 5
1 / -0

The figure below shows a body of mass 10 kg sliding from rest, down a frictionless track of radius R (in m). Assume that the body started from the top of the track P and slides to the bottom Q. The change in the gravitational potential energy in the motion is (g = acceleration due to gravity)

A
g/2 J

B
10 J

C
10gR J

D
10R J

Solution

The body descends a height R.
The change in the gravitational potential energy would be 'mgh'.
Here, 'm' is the mass of the body, 'g' is the acceleration due to gravity and 'h' is the height.
⇒ mgh for the body would be 10gR J.
Question 6
1 / -0

A concave mirror of focal length f produces an image m times the size of the object. If the image is real, then the distance of the object from the mirror is

A
(m – 1)f

B

C

D
(m + 1)f

Solution

For the mirror
Question 7
1 / -0

If refractive index for glass is 1.5, and the velocity of light in vacuum is 3.0 ×10⁸ m/sec, the time taken by the light in travelling a distance of 300 m in glass will be

A
1.4 ×10^-4 s

B
1.5 ×10^-5 s

C
1.5 ×10^-6 s

D
1.5 ×10^-7 s

Solution

1.5 = 3 × 10⁸/300 × t
t = 1.5 × 10^-6 sec
Question 8
1 / -0

Gravity is a conservative force. Which of the following is incorrect about this force?

A
Force always points towards a certain point in space.

B
The work done on moving a particle from one point to another doesn't depend on path.

C
Mechanical energy remains constant.

D
Kinetic energy of a system under the influence of gravity remains constant.

Solution

Kinetic energy depends upon the speed and mass of the body. More massive objects would have more kinetic energy than other objects of the same mass.
Question 9
1 / -0

At what height above the earth's surface does the acceleration due to gravity fall to 1% of its value at the earth's surface?

A
9R

B
10R

C
99R

D
100R

Solution

GM/R² = 9.8 m/s²

g/100 = 1.1% of g means the denominator of the first equation will be 100 times R²

100R² = (10R)² = (h + R)² (where h is the altitude)

10R = h + R

9R = h
Question 10
1 / -0

A and B are two objects. The temperature of A is greater than that of B. This means that

A
the molecules of A are moving faster on the average than that of B

B
the total energy of A is greater than that of B

C
the average potential energy of A is greater than that of B

D
the heat content of A will always be greater than that of B

Solution

The temperature of an object is a property of the object that determines how hot or cold the body is. It depends on the amount of thermal energy absorbed by the object and also the nature of the object and its mass. Moreover, movement of molecules in an object increases the heat. More the movement, more will be the temperature.
Question 11
1 / -0

A particle has an initial velocity of 9 m/s due east and a constant acceleration of 2 m/s² due west. The distance covered by the particle in the 5^thsecond of its motion is

A
0

B
0.5 m

C
2 m

D
None of these

Solution

To find the distance, it is to be determined first if the particle has changed its direction during the course of motion. This can be determine by knowing the time of zero velocity. If this time lies within the interval of interest, the time interval should be divided into two parts, the distance should be calculated seperately and then the total distance is the summation of these distances.
Question 12
1 / -0

A particle moves along the x- axis as follows:

It starts from rest at t = 0 from a point x = 0 and comes to rest at t = 1 at a point x = 1. No other information is available about its motion for the intermediate time (0 < t < 1). If α denotes the instantaneous acceleration of the particle, then

A
α cannot remain positive for all t in the interval 0 ≤ t ≤ 1

B
|α| cannot exceed 2 at any point in its path

C
|α| can never be ≥ 4

D
α must change sign during the motion, but no other assertion can be made with the information given

Solution

The motion of the particle is simple harmonic. The particle is at one extreme position x = 0 at t = 0 and at the other extreme position at x = 1 unit at t = 1s.
Therefore, the time period of the motion is T = 2s and its amplitude A = 1/2 unit.
Therefore, angular frequency is ω = 2π/T = 2π/2 = π rad s^-1.

∴ Maximum acceleration is α_max= ω²A = (π)²× 1/2
Thus, the value of α can exceed 2 and can be greater than 4 at some points in the path of the particle.
Further, in simple harmonic motion, α changes sign and cannot remain positive in the time interval 0 ≤ t ≤ 1s.
Question 13
1 / -0

Ultrasonic, infrasonic and audible waves travel through a medium with speeds v_u, v_i and v_a,respectively. Which of the following relations holds true?

A
v_i = v_a = v_u

B
v_u > v_a > v_i

C
v_u < v_a < v_i

D
v_a ≤ v_u ≤ v_i

Solution

All the three waves will travel with the same speed. The difference lies in their wavelengths and frequencies.
Question 14
1 / -0

Which of the following salts possesses water of crystallisation?

A
Calcium hypochlorite

B
Gypsum

C
Ammonium chloride

D
Sodium bicarbonate

Solution

Gypsum is calcium sulphate dihydrate and possesses two molecules of water of crystallisation in its structure, i.e. CaSO₄.2H₂O.
Question 15
1 / -0

Which of the following is basic in nature?

A
CaO

B
CO₂

C
SO₃

D
HCl

Solution

CaO is basic in nature as the oxides of alkali metals (1^st group) and alkaline metals (2^nd group) are basic oxides.