360035
The mass of earth is 81 times the mass of moon and the distance between their centres is \(R\). The distance from the centre of the earth, where gravitational force will be zero is
1 \(\dfrac{R}{4}\)
2 \(\dfrac{R}{2}\)
3 \(\dfrac{9 R}{10}\)
4 \(\dfrac{R}{81}\)
Explanation:
Let \(x\) be the distance of the point from the centre of earth, where gravitational force is zero. The gravitational field intensities due to earth and moon will have same magnitudes at that point. Hence, \(\dfrac{G \times(81 m)}{(x)^{2}}=\dfrac{G \times(m)}{(R-x)^{2}}\) \(\Rightarrow \dfrac{81}{(x)^{2}}=\dfrac{1}{(R-x)^{2}}\) \(\Rightarrow 81(R-x)^{2}-x^{2}=0 \Rightarrow(9 R-8 x)(9 R-10 x)=0\) \(\Rightarrow x=\dfrac{9 R}{10}, \text { and } x=\dfrac{9 R}{8}\)
MHTCET - 2020
PHXI08:GRAVITATION
360036
Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to
1 \(R^{2}\)
2 \(R^{-4}\)
3 \(R^{4}\)
4 \(R^{-2}\)
Explanation:
\(F=\dfrac{G \times m \times m}{(2 R)^{2}}=\dfrac{G \times\left(\dfrac{4}{3} \pi R^{3} \rho\right)^{2}}{4 R^{2}}\) \(=\dfrac{4}{9} \pi^{2} \rho^{2} R^{4} \Rightarrow F \propto R^{4}\)
PHXI08:GRAVITATION
360037
Two heavenly bodies \({s_1}\) & \({s_2}\) not far off from each other, revolve in space
1 Around their common centre of mass
2 \({s_1}\) is fixed and \({s_2}\) revolves around \({s_1}\)
3 \(s_{2}\) is fixed and \(s_{1}\) revolves around \(s_{2}\)
4 We cannot say anything
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360038
Among the following the wrong statement is?
1 Gravitational force is conservative in nature.
2 Law of gravitation cannot explain why gravity exists
3 Law of gravitation does not explain the presence of force even when the particles are not in physical contact
4 When the range is long, gravitational force becomes repulsive.
360035
The mass of earth is 81 times the mass of moon and the distance between their centres is \(R\). The distance from the centre of the earth, where gravitational force will be zero is
1 \(\dfrac{R}{4}\)
2 \(\dfrac{R}{2}\)
3 \(\dfrac{9 R}{10}\)
4 \(\dfrac{R}{81}\)
Explanation:
Let \(x\) be the distance of the point from the centre of earth, where gravitational force is zero. The gravitational field intensities due to earth and moon will have same magnitudes at that point. Hence, \(\dfrac{G \times(81 m)}{(x)^{2}}=\dfrac{G \times(m)}{(R-x)^{2}}\) \(\Rightarrow \dfrac{81}{(x)^{2}}=\dfrac{1}{(R-x)^{2}}\) \(\Rightarrow 81(R-x)^{2}-x^{2}=0 \Rightarrow(9 R-8 x)(9 R-10 x)=0\) \(\Rightarrow x=\dfrac{9 R}{10}, \text { and } x=\dfrac{9 R}{8}\)
MHTCET - 2020
PHXI08:GRAVITATION
360036
Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to
1 \(R^{2}\)
2 \(R^{-4}\)
3 \(R^{4}\)
4 \(R^{-2}\)
Explanation:
\(F=\dfrac{G \times m \times m}{(2 R)^{2}}=\dfrac{G \times\left(\dfrac{4}{3} \pi R^{3} \rho\right)^{2}}{4 R^{2}}\) \(=\dfrac{4}{9} \pi^{2} \rho^{2} R^{4} \Rightarrow F \propto R^{4}\)
PHXI08:GRAVITATION
360037
Two heavenly bodies \({s_1}\) & \({s_2}\) not far off from each other, revolve in space
1 Around their common centre of mass
2 \({s_1}\) is fixed and \({s_2}\) revolves around \({s_1}\)
3 \(s_{2}\) is fixed and \(s_{1}\) revolves around \(s_{2}\)
4 We cannot say anything
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360038
Among the following the wrong statement is?
1 Gravitational force is conservative in nature.
2 Law of gravitation cannot explain why gravity exists
3 Law of gravitation does not explain the presence of force even when the particles are not in physical contact
4 When the range is long, gravitational force becomes repulsive.
360035
The mass of earth is 81 times the mass of moon and the distance between their centres is \(R\). The distance from the centre of the earth, where gravitational force will be zero is
1 \(\dfrac{R}{4}\)
2 \(\dfrac{R}{2}\)
3 \(\dfrac{9 R}{10}\)
4 \(\dfrac{R}{81}\)
Explanation:
Let \(x\) be the distance of the point from the centre of earth, where gravitational force is zero. The gravitational field intensities due to earth and moon will have same magnitudes at that point. Hence, \(\dfrac{G \times(81 m)}{(x)^{2}}=\dfrac{G \times(m)}{(R-x)^{2}}\) \(\Rightarrow \dfrac{81}{(x)^{2}}=\dfrac{1}{(R-x)^{2}}\) \(\Rightarrow 81(R-x)^{2}-x^{2}=0 \Rightarrow(9 R-8 x)(9 R-10 x)=0\) \(\Rightarrow x=\dfrac{9 R}{10}, \text { and } x=\dfrac{9 R}{8}\)
MHTCET - 2020
PHXI08:GRAVITATION
360036
Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to
1 \(R^{2}\)
2 \(R^{-4}\)
3 \(R^{4}\)
4 \(R^{-2}\)
Explanation:
\(F=\dfrac{G \times m \times m}{(2 R)^{2}}=\dfrac{G \times\left(\dfrac{4}{3} \pi R^{3} \rho\right)^{2}}{4 R^{2}}\) \(=\dfrac{4}{9} \pi^{2} \rho^{2} R^{4} \Rightarrow F \propto R^{4}\)
PHXI08:GRAVITATION
360037
Two heavenly bodies \({s_1}\) & \({s_2}\) not far off from each other, revolve in space
1 Around their common centre of mass
2 \({s_1}\) is fixed and \({s_2}\) revolves around \({s_1}\)
3 \(s_{2}\) is fixed and \(s_{1}\) revolves around \(s_{2}\)
4 We cannot say anything
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360038
Among the following the wrong statement is?
1 Gravitational force is conservative in nature.
2 Law of gravitation cannot explain why gravity exists
3 Law of gravitation does not explain the presence of force even when the particles are not in physical contact
4 When the range is long, gravitational force becomes repulsive.
360035
The mass of earth is 81 times the mass of moon and the distance between their centres is \(R\). The distance from the centre of the earth, where gravitational force will be zero is
1 \(\dfrac{R}{4}\)
2 \(\dfrac{R}{2}\)
3 \(\dfrac{9 R}{10}\)
4 \(\dfrac{R}{81}\)
Explanation:
Let \(x\) be the distance of the point from the centre of earth, where gravitational force is zero. The gravitational field intensities due to earth and moon will have same magnitudes at that point. Hence, \(\dfrac{G \times(81 m)}{(x)^{2}}=\dfrac{G \times(m)}{(R-x)^{2}}\) \(\Rightarrow \dfrac{81}{(x)^{2}}=\dfrac{1}{(R-x)^{2}}\) \(\Rightarrow 81(R-x)^{2}-x^{2}=0 \Rightarrow(9 R-8 x)(9 R-10 x)=0\) \(\Rightarrow x=\dfrac{9 R}{10}, \text { and } x=\dfrac{9 R}{8}\)
MHTCET - 2020
PHXI08:GRAVITATION
360036
Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to
1 \(R^{2}\)
2 \(R^{-4}\)
3 \(R^{4}\)
4 \(R^{-2}\)
Explanation:
\(F=\dfrac{G \times m \times m}{(2 R)^{2}}=\dfrac{G \times\left(\dfrac{4}{3} \pi R^{3} \rho\right)^{2}}{4 R^{2}}\) \(=\dfrac{4}{9} \pi^{2} \rho^{2} R^{4} \Rightarrow F \propto R^{4}\)
PHXI08:GRAVITATION
360037
Two heavenly bodies \({s_1}\) & \({s_2}\) not far off from each other, revolve in space
1 Around their common centre of mass
2 \({s_1}\) is fixed and \({s_2}\) revolves around \({s_1}\)
3 \(s_{2}\) is fixed and \(s_{1}\) revolves around \(s_{2}\)
4 We cannot say anything
Explanation:
Conceptual Question
PHXI08:GRAVITATION
360038
Among the following the wrong statement is?
1 Gravitational force is conservative in nature.
2 Law of gravitation cannot explain why gravity exists
3 Law of gravitation does not explain the presence of force even when the particles are not in physical contact
4 When the range is long, gravitational force becomes repulsive.
