Major Competitive Exams
Q. If the mass of an object is measured as 10.0 kg with an uncertainty of ±0.2 kg, what is the percentage error?
A.
2%
B.
0.2%
C.
0.02%
D.
0.5%
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Solution
Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.
Correct Answer: A — 2%
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Q. If the mass of an object is measured as 10.0 kg with an uncertainty of ±0.2 kg, what is the percentage error in the mass measurement?
A.
2%
B.
0.2%
C.
0.5%
D.
1%
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Solution
Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.
Correct Answer: D — 1%
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Q. If the mass of an object is measured as 50 kg with an uncertainty of ±0.5 kg, what is the percentage error in the mass measurement?
A.
1%
B.
0.1%
C.
0.5%
D.
2%
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Solution
Percentage error = (absolute error / measured value) * 100 = (0.5 / 50) * 100 = 1%.
Correct Answer: A — 1%
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Q. If the mass of an object is measured in kilograms and its volume in cubic meters, what is the unit of density? (2022)
A.
kg/m
B.
kg/m^3
C.
m^3/kg
D.
m/kg
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Solution
Density is defined as mass per unit volume, so the unit of density is kg/m³.
Correct Answer: B — kg/m^3
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Q. If the mass of an object is tripled, how does its gravitational potential energy change at a constant height?
A.
It triples
B.
It doubles
C.
It remains the same
D.
It increases by a factor of nine
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Solution
Gravitational potential energy U = mgh, so if mass is tripled, U also triples.
Correct Answer: A — It triples
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Q. If the mass of an object is tripled, how does the gravitational potential energy change for a constant height?
A.
It triples
B.
It doubles
C.
It halves
D.
It remains the same
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Solution
Gravitational potential energy is directly proportional to mass, so it triples.
Correct Answer: A — It triples
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Q. If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational acceleration at the surface of the Earth?
A.
9.8 m/s²
B.
10 m/s²
C.
9.81 m/s²
D.
11 m/s²
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Solution
Using g = G * M / R², where G = 6.67 x 10^-11 N m²/kg², M = 6 x 10^24 kg, and R = 6.4 x 10^6 m, we find g ≈ 9.8 m/s².
Correct Answer: A — 9.8 m/s²
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Q. If the mass of the Earth is 6 x 10^24 kg and the radius is 6.4 x 10^6 m, what is the gravitational force on a 1 kg mass at the surface?
A.
9.8 N
B.
6.67 N
C.
10 N
D.
8.9 N
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Solution
Using F = G * (m1 * m2) / r^2, F = (6.67 x 10^-11) * (6 x 10^24 * 1) / (6.4 x 10^6)^2 = 9.8 N.
Correct Answer: A — 9.8 N
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Q. If the mass of the Earth is 6 × 10^24 kg and its radius is 6.4 × 10^6 m, what is the acceleration due to gravity at its surface?
A.
9.8 m/s²
B.
10 m/s²
C.
9.81 m/s²
D.
8.9 m/s²
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Solution
g = G * M / R² = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)² = 9.81 m/s²
Correct Answer: C — 9.81 m/s²
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Q. If the mass of the Earth is M and its radius is R, what is the gravitational acceleration at the surface of the Earth?
A.
g = GM/R^2
B.
g = GMR^2
C.
g = G/MR^2
D.
g = MR/G
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Solution
The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.
Correct Answer: A — g = GM/R^2
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Q. If the mass of the Earth is M and the radius is R, what is the gravitational acceleration at the surface of the Earth?
A.
g = GM/R^2
B.
g = GMR^2
C.
g = G/R
D.
g = M/R^2
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Solution
The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.
Correct Answer: A — g = GM/R^2
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Q. If the mass of the Earth is M and the radius is R, what is the gravitational force acting on a satellite of mass m at a height h?
A.
GmM/R^2
B.
GmM/(R+h)^2
C.
GmM/(R-h)^2
D.
GmM/h^2
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Solution
The gravitational force F acting on a satellite at height h is given by F = GmM/(R+h)^2, where G is the gravitational constant.
Correct Answer: B — GmM/(R+h)^2
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Q. If the mass of the Earth were to double while its radius remained the same, what would happen to the gravitational acceleration at its surface?
A.
It would double
B.
It would remain the same
C.
It would halve
D.
It would increase by a factor of four
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Solution
Gravitational acceleration is directly proportional to mass, so if the mass doubles, g also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double while its radius remains the same, what would happen to the gravitational acceleration at its surface?
A.
It would double
B.
It would remain the same
C.
It would halve
D.
It would increase by a factor of four
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Solution
Gravitational acceleration is directly proportional to mass; thus, if the mass doubles, g also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double while its radius remains the same, what would happen to the acceleration due to gravity? (2022)
A.
It would double
B.
It would remain the same
C.
It would halve
D.
It would increase by a factor of four
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Solution
If the mass of the Earth doubles, the acceleration due to gravity also doubles, as it is directly proportional to mass.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double while the radius remains the same, what would happen to the weight of an object on its surface?
A.
It would double
B.
It would remain the same
C.
It would increase by a factor of four
D.
It would decrease by half
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Solution
Weight is proportional to mass; thus, if the Earth's mass doubles, the weight of an object on its surface also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?
A.
It would double
B.
It would remain the same
C.
It would increase by a factor of four
D.
It would decrease by half
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Solution
If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the gravitational force experienced by an object on its surface?
A.
It doubles
B.
It halves
C.
It quadruples
D.
It remains the same
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Solution
Gravitational force is directly proportional to mass. If mass doubles, force also doubles.
Correct Answer: A — It doubles
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Q. If the mass of the Earth were to double, what would happen to the gravitational force between two objects on its surface?
A.
It would double
B.
It would remain the same
C.
It would be halved
D.
It would quadruple
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Solution
F = G * (m1 * m2) / r², doubling the mass of Earth doubles the force.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the gravitational force between the Earth and an object on its surface?
A.
It would double
B.
It would remain the same
C.
It would halve
D.
It would quadruple
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Solution
F ∝ M; if M doubles, F also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to double, what would happen to the weight of an object on its surface?
A.
It would double
B.
It would remain the same
C.
It would be halved
D.
It would be quartered
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Solution
Weight is directly proportional to mass. If the Earth's mass doubles, the weight of the object also doubles.
Correct Answer: A — It would double
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Q. If the mass of the Earth were to increase while the radius remains constant, what would happen to the gravitational force experienced by an object on its surface?
A.
It would decrease
B.
It would increase
C.
It would remain the same
D.
It would become zero
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Solution
If the mass of the Earth increases, the gravitational force experienced by an object on its surface would increase.
Correct Answer: B — It would increase
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Q. If the mean of a data set is 12 and there are 8 values, what is the total sum of the values?
A.
80
B.
90
C.
100
D.
110
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Solution
Total sum = Mean * Number of values = 12 * 8 = 96.
Correct Answer: A — 80
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Q. If the mean of a data set is 20 and the standard deviation is 4, what is the coefficient of variation?
A.
20%
B.
25%
C.
15%
D.
10%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4 / 20) * 100 = 20%.
Correct Answer: B — 25%
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Q. If the mean of a data set is 30 and there are 10 values, what is the total sum of the values?
A.
300
B.
310
C.
320
D.
330
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Solution
Total sum = Mean * Number of values = 30 * 10 = 300.
Correct Answer: A — 300
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Q. If the mean of a data set is 50 and the standard deviation is 10, what is the coefficient of variation?
A.
20%
B.
10%
C.
15%
D.
25%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (10 / 50) * 100 = 20%.
Correct Answer: A — 20%
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Q. If the mean of a data set is 50 and there are 10 values, what is the total sum of the values?
A.
500
B.
600
C.
700
D.
800
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Solution
Total sum = Mean * Number of values = 50 * 10 = 500.
Correct Answer: A — 500
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Q. If the mean of a dataset is 50 and there are 10 numbers, what is the total sum of the numbers? (2021)
A.
500
B.
600
C.
550
D.
450
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Solution
Total sum = Mean * Number of elements = 50 * 10 = 500.
Correct Answer: A — 500
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Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)
A.
180
B.
150
C.
120
D.
200
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Solution
Total sum = Mean * Number of elements = 30 * 6 = 180.
Correct Answer: A — 180
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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)
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Solution
Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.
Correct Answer: A — 30
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