360065
Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\dfrac{2 \sqrt{2}+1}{32}\right) \dfrac{G m^{2}}{L^{2}}\), the length of the sides of the square is
1 \(\dfrac{L}{2}\)
2 \(4\,L\)
3 \(3\,L\)
4 \(2\,L\)
Explanation:
The force on one mass by other masses \(F_{\text {Net }}=\dfrac{G m^{2}}{2 x^{2}}+\sqrt{\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}+\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}}\) \(=\dfrac{G m^{2}}{2 x^{2}}+\dfrac{G m^{2} \sqrt{2}}{x^{2}}=\dfrac{G m^{2}}{x^{2}}\left(\dfrac{1}{2}+\sqrt{2}\right)\) On comparing with the given value of force, \(x^{2}=16 L^{2} \Rightarrow x=4 L\)
JEE - 2024
PHXI08:GRAVITATION
360066
Attractive force exists between two protons inside the nucleus, this is due to
1 Gravitational Forces
2 Electro magnetic Forces
3 Weak Nuclear Forces
4 Strong Nuclear Forces
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360067
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon
1 Will be elliptical
2 Will not be strictly elliptical because the total gravitational force on it is not central
3 Is not eliptical but will necessarily be a closed curve.
4 Deviates considerably from being elliptical due to influence of planets other than earth
Explanation:
Moon is revolving around earth in almost circular orbit. Sun exerts gravitational pull on both, earth and moon. When observed from sun, the orbit of the moon will not be strictly elliptical because the total gravitational force (i.e., force due to earth on moon and fource due to sun on moon) is not central.
360065
Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\dfrac{2 \sqrt{2}+1}{32}\right) \dfrac{G m^{2}}{L^{2}}\), the length of the sides of the square is
1 \(\dfrac{L}{2}\)
2 \(4\,L\)
3 \(3\,L\)
4 \(2\,L\)
Explanation:
The force on one mass by other masses \(F_{\text {Net }}=\dfrac{G m^{2}}{2 x^{2}}+\sqrt{\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}+\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}}\) \(=\dfrac{G m^{2}}{2 x^{2}}+\dfrac{G m^{2} \sqrt{2}}{x^{2}}=\dfrac{G m^{2}}{x^{2}}\left(\dfrac{1}{2}+\sqrt{2}\right)\) On comparing with the given value of force, \(x^{2}=16 L^{2} \Rightarrow x=4 L\)
JEE - 2024
PHXI08:GRAVITATION
360066
Attractive force exists between two protons inside the nucleus, this is due to
1 Gravitational Forces
2 Electro magnetic Forces
3 Weak Nuclear Forces
4 Strong Nuclear Forces
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360067
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon
1 Will be elliptical
2 Will not be strictly elliptical because the total gravitational force on it is not central
3 Is not eliptical but will necessarily be a closed curve.
4 Deviates considerably from being elliptical due to influence of planets other than earth
Explanation:
Moon is revolving around earth in almost circular orbit. Sun exerts gravitational pull on both, earth and moon. When observed from sun, the orbit of the moon will not be strictly elliptical because the total gravitational force (i.e., force due to earth on moon and fource due to sun on moon) is not central.
360065
Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\dfrac{2 \sqrt{2}+1}{32}\right) \dfrac{G m^{2}}{L^{2}}\), the length of the sides of the square is
1 \(\dfrac{L}{2}\)
2 \(4\,L\)
3 \(3\,L\)
4 \(2\,L\)
Explanation:
The force on one mass by other masses \(F_{\text {Net }}=\dfrac{G m^{2}}{2 x^{2}}+\sqrt{\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}+\left(\dfrac{G m^{2}}{x^{2}}\right)^{2}}\) \(=\dfrac{G m^{2}}{2 x^{2}}+\dfrac{G m^{2} \sqrt{2}}{x^{2}}=\dfrac{G m^{2}}{x^{2}}\left(\dfrac{1}{2}+\sqrt{2}\right)\) On comparing with the given value of force, \(x^{2}=16 L^{2} \Rightarrow x=4 L\)
JEE - 2024
PHXI08:GRAVITATION
360066
Attractive force exists between two protons inside the nucleus, this is due to
1 Gravitational Forces
2 Electro magnetic Forces
3 Weak Nuclear Forces
4 Strong Nuclear Forces
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360067
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon
1 Will be elliptical
2 Will not be strictly elliptical because the total gravitational force on it is not central
3 Is not eliptical but will necessarily be a closed curve.
4 Deviates considerably from being elliptical due to influence of planets other than earth
Explanation:
Moon is revolving around earth in almost circular orbit. Sun exerts gravitational pull on both, earth and moon. When observed from sun, the orbit of the moon will not be strictly elliptical because the total gravitational force (i.e., force due to earth on moon and fource due to sun on moon) is not central.
