To solve this problem, we need to calculate the force of attraction between two masses using Newton's law of universal gravitation. The formula is given by:
\(F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}}\)
- \(F\) is the force of attraction between the two bodies.
- \(G\) is the gravitational constant, approximately \(6.674 \times 10^{-11}\ \text{N m}^2/\text{kg}^2\).
- \(m_1\) and \(m_2\) are the masses of the two bodies; in this case, \(20 \ \text{kg}\) and \(50\ \text{kg}\) respectively.
- \(r\) is the distance between the centers of the two masses, given as \(2\ \text{m}\).
Let's substitute the given values into the formula:
\(F = \frac{{6.674 \times 10^{-11}\ \text{N m}^2/\text{kg}^2 \cdot 20\ \text{kg} \cdot 50\ \text{kg}}}{{(2\ \text{m})^2}}\)
\(F = \frac{{6.674 \times 10^{-11} \cdot 20 \cdot 50}}{{4}} \text{N}\)
Calculating further:
\(F = \frac{{6.674 \times 10^{-11} \cdot 1000}}{{4}}\ N\)
\(F = \frac{{6.674 \times 10^{-8}}}{{4}}\ N\)
\(F = 1.6685 \times 10^{-8}\ N\)
Converting \(1.6685 \times 10^{-8}\ N\) to match one of the answer options:
\(1.6685 \times 10^{-8}\ N = 166.85 \times 10^{-10}\ N\)
Thus, the closest answer option is \(166.75 \times 10^{-10}\ N\).
Therefore, the correct answer is: $166.75 \times 10^{-10}\ N$.
Similar Questions
The gravitational force between two objects of masses m1 and m2 is directly proportional to
The force exerted by the earth on the moon is:
(Consider G=\(6 \times 10^{-11}Nm^2kg^{-2}\) ; mass of the earth M=\(6 \times 10^{24}\)kg; mass of the moon= \(8 \times 10^{22}\) kg, and distance between earth and moon is \(4 \times 10^{8}\) m).Which of the following statements is/are correct?
Statements:
I) The mass of an object is the same as its weight.
II) The mass of an object is not the same as its weight.
III) Mass is scalar quantity, whereas weight is vector quantity.
Which of the following statements is/are correct?
Statements:
I) The Gravitational force between two objects is independent of the distance of separation between two objects.
II) The Gravitational force between two objects is inversely proportional to the square of the distance of the separation between two objects.
III) The Gravitational force between two objects is directly proportional to the product of their masses.
When an object falls under gravity, the object experiences:
If the acceleration due to gravity of the earth is 6 times the acceleration due to gravity on the moon, which of the following statements is correct?
Energy possessed by a body by virtue of its position or configuration is:
- Which of the following statements is/are INCORRECT?
A. The value of G on the moon is equal to that on the earth.
B. $26.68 \times 10^{-11}$ N is the force of gravitation between two point masses of 2 kg and 2 kg kept 1 m apart.
C. Newton's law of gravitation is valid in the laboratory only.
D. Force is inversely proportional to the square of the distance between two bodies.
Important Questions from Gravitation
The known forces of nature can be divided into four classes, viz., gravity, electromagnetism, weak nuclear force and strong nuclear force. With reference to them, which one of the following statements is not correct?
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The force of attraction between two bodies separated by a distance of d is F. The distance for which the force of attraction between them is 64 F is ________.
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