360018
\({F_g},{F_e}\) and \({F_n}\) represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths
1 \({F_n},{F_e},{F_g}\)
2 \({F_g},{F_e},{F_n}\)
3 \({F_e},{F_g},{F_n}\)
4 \({F_g},{F_n},{F_e}\)
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360019
Three masses, each equal to \(M\), are placed at the three corners of a square of side \(a\). The force of attraction on unit mass at the fourth corner will be
\(F_{1}=F_{2}=\dfrac{G M}{a^{2}}\) Resultant of \(F_{1}\) and \(F_{2}\) is \(\sqrt{2} \dfrac{G M}{a^{2}}\) Now, \(\quad F_{3}=\dfrac{G M}{(\sqrt{2} a)^{2}}=\dfrac{G M}{2 a^{2}}\) Now, \(\dfrac{\sqrt{2} G M}{a^{2}}\) and \(\dfrac{G M}{2 a^{2}}\) act in the same direction. Their resultant is \(\dfrac{G M}{a^{2}}\left[\sqrt{2}+\dfrac{1}{2}\right]\)
PHXI08:GRAVITATION
360020
Particles of masses \(2M,m\) and \(M\) are respectively at points \(A\), \(B\) and \(C\) with \(AB = \frac{1}{2}(BC),m\) is much smaller than \(M\) and at time \(t=0\), they are all at rest as given in figure. At subsequent times before any collision takes place.
1 \(m\) will remain at rest
2 \(m\) will move towards \(M\)
3 \(m\) will move towards 2\(M\)
4 \(m\) will have oscillatory motion
Explanation:
Resultant force on mass \(m\) due to masses at \(A\) and \(C\) is \(F=\dfrac{G 2 M \times m}{\left(A B^{2}\right)}-\dfrac{G M m}{\left(B C^{2}\right)}\). Therfore, \(m\) will move towards 2\(M\).
NCERT Exemplar
PHXI08:GRAVITATION
360021
An astronaut of mass \(m\) is working on a satellite orbiting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_{G}\) on the astronaut is
1 Zero since astronaut feels weightless
2 \(\dfrac{G M m}{(R+h)^{2}} < F_{G} < \dfrac{G M m}{R^{2}}\)
3 \(F_{G}=\dfrac{G M m}{(R+h)^{2}}\)
4 \(0 < F_{G} < \dfrac{G M m}{R^{2}}\)
Explanation:
Gravitational force \(F=\dfrac{G M m}{(R+h)^{2}}\)
360018
\({F_g},{F_e}\) and \({F_n}\) represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths
1 \({F_n},{F_e},{F_g}\)
2 \({F_g},{F_e},{F_n}\)
3 \({F_e},{F_g},{F_n}\)
4 \({F_g},{F_n},{F_e}\)
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360019
Three masses, each equal to \(M\), are placed at the three corners of a square of side \(a\). The force of attraction on unit mass at the fourth corner will be
\(F_{1}=F_{2}=\dfrac{G M}{a^{2}}\) Resultant of \(F_{1}\) and \(F_{2}\) is \(\sqrt{2} \dfrac{G M}{a^{2}}\) Now, \(\quad F_{3}=\dfrac{G M}{(\sqrt{2} a)^{2}}=\dfrac{G M}{2 a^{2}}\) Now, \(\dfrac{\sqrt{2} G M}{a^{2}}\) and \(\dfrac{G M}{2 a^{2}}\) act in the same direction. Their resultant is \(\dfrac{G M}{a^{2}}\left[\sqrt{2}+\dfrac{1}{2}\right]\)
PHXI08:GRAVITATION
360020
Particles of masses \(2M,m\) and \(M\) are respectively at points \(A\), \(B\) and \(C\) with \(AB = \frac{1}{2}(BC),m\) is much smaller than \(M\) and at time \(t=0\), they are all at rest as given in figure. At subsequent times before any collision takes place.
1 \(m\) will remain at rest
2 \(m\) will move towards \(M\)
3 \(m\) will move towards 2\(M\)
4 \(m\) will have oscillatory motion
Explanation:
Resultant force on mass \(m\) due to masses at \(A\) and \(C\) is \(F=\dfrac{G 2 M \times m}{\left(A B^{2}\right)}-\dfrac{G M m}{\left(B C^{2}\right)}\). Therfore, \(m\) will move towards 2\(M\).
NCERT Exemplar
PHXI08:GRAVITATION
360021
An astronaut of mass \(m\) is working on a satellite orbiting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_{G}\) on the astronaut is
1 Zero since astronaut feels weightless
2 \(\dfrac{G M m}{(R+h)^{2}} < F_{G} < \dfrac{G M m}{R^{2}}\)
3 \(F_{G}=\dfrac{G M m}{(R+h)^{2}}\)
4 \(0 < F_{G} < \dfrac{G M m}{R^{2}}\)
Explanation:
Gravitational force \(F=\dfrac{G M m}{(R+h)^{2}}\)
360018
\({F_g},{F_e}\) and \({F_n}\) represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths
1 \({F_n},{F_e},{F_g}\)
2 \({F_g},{F_e},{F_n}\)
3 \({F_e},{F_g},{F_n}\)
4 \({F_g},{F_n},{F_e}\)
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360019
Three masses, each equal to \(M\), are placed at the three corners of a square of side \(a\). The force of attraction on unit mass at the fourth corner will be
\(F_{1}=F_{2}=\dfrac{G M}{a^{2}}\) Resultant of \(F_{1}\) and \(F_{2}\) is \(\sqrt{2} \dfrac{G M}{a^{2}}\) Now, \(\quad F_{3}=\dfrac{G M}{(\sqrt{2} a)^{2}}=\dfrac{G M}{2 a^{2}}\) Now, \(\dfrac{\sqrt{2} G M}{a^{2}}\) and \(\dfrac{G M}{2 a^{2}}\) act in the same direction. Their resultant is \(\dfrac{G M}{a^{2}}\left[\sqrt{2}+\dfrac{1}{2}\right]\)
PHXI08:GRAVITATION
360020
Particles of masses \(2M,m\) and \(M\) are respectively at points \(A\), \(B\) and \(C\) with \(AB = \frac{1}{2}(BC),m\) is much smaller than \(M\) and at time \(t=0\), they are all at rest as given in figure. At subsequent times before any collision takes place.
1 \(m\) will remain at rest
2 \(m\) will move towards \(M\)
3 \(m\) will move towards 2\(M\)
4 \(m\) will have oscillatory motion
Explanation:
Resultant force on mass \(m\) due to masses at \(A\) and \(C\) is \(F=\dfrac{G 2 M \times m}{\left(A B^{2}\right)}-\dfrac{G M m}{\left(B C^{2}\right)}\). Therfore, \(m\) will move towards 2\(M\).
NCERT Exemplar
PHXI08:GRAVITATION
360021
An astronaut of mass \(m\) is working on a satellite orbiting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_{G}\) on the astronaut is
1 Zero since astronaut feels weightless
2 \(\dfrac{G M m}{(R+h)^{2}} < F_{G} < \dfrac{G M m}{R^{2}}\)
3 \(F_{G}=\dfrac{G M m}{(R+h)^{2}}\)
4 \(0 < F_{G} < \dfrac{G M m}{R^{2}}\)
Explanation:
Gravitational force \(F=\dfrac{G M m}{(R+h)^{2}}\)
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PHXI08:GRAVITATION
360018
\({F_g},{F_e}\) and \({F_n}\) represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths
1 \({F_n},{F_e},{F_g}\)
2 \({F_g},{F_e},{F_n}\)
3 \({F_e},{F_g},{F_n}\)
4 \({F_g},{F_n},{F_e}\)
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360019
Three masses, each equal to \(M\), are placed at the three corners of a square of side \(a\). The force of attraction on unit mass at the fourth corner will be
\(F_{1}=F_{2}=\dfrac{G M}{a^{2}}\) Resultant of \(F_{1}\) and \(F_{2}\) is \(\sqrt{2} \dfrac{G M}{a^{2}}\) Now, \(\quad F_{3}=\dfrac{G M}{(\sqrt{2} a)^{2}}=\dfrac{G M}{2 a^{2}}\) Now, \(\dfrac{\sqrt{2} G M}{a^{2}}\) and \(\dfrac{G M}{2 a^{2}}\) act in the same direction. Their resultant is \(\dfrac{G M}{a^{2}}\left[\sqrt{2}+\dfrac{1}{2}\right]\)
PHXI08:GRAVITATION
360020
Particles of masses \(2M,m\) and \(M\) are respectively at points \(A\), \(B\) and \(C\) with \(AB = \frac{1}{2}(BC),m\) is much smaller than \(M\) and at time \(t=0\), they are all at rest as given in figure. At subsequent times before any collision takes place.
1 \(m\) will remain at rest
2 \(m\) will move towards \(M\)
3 \(m\) will move towards 2\(M\)
4 \(m\) will have oscillatory motion
Explanation:
Resultant force on mass \(m\) due to masses at \(A\) and \(C\) is \(F=\dfrac{G 2 M \times m}{\left(A B^{2}\right)}-\dfrac{G M m}{\left(B C^{2}\right)}\). Therfore, \(m\) will move towards 2\(M\).
NCERT Exemplar
PHXI08:GRAVITATION
360021
An astronaut of mass \(m\) is working on a satellite orbiting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_{G}\) on the astronaut is
1 Zero since astronaut feels weightless
2 \(\dfrac{G M m}{(R+h)^{2}} < F_{G} < \dfrac{G M m}{R^{2}}\)
3 \(F_{G}=\dfrac{G M m}{(R+h)^{2}}\)
4 \(0 < F_{G} < \dfrac{G M m}{R^{2}}\)
Explanation:
Gravitational force \(F=\dfrac{G M m}{(R+h)^{2}}\)
