Mass: Mass is a measure of the amount of matter in an object. It is a scalar quantity and is typically measured in kilograms (kg) or grams (g). Mass does not change regardless of the object's location in the universe.
Weight: Weight is the force exerted by gravity on an object. It is a vector quantity and depends on both the mass of the object and the gravitational acceleration. The formula for weight is: \[ \text{Weight} = \text{Mass} \times \text{Gravitational acceleration} \] Weight varies depending on the location of the object (for example, on Earth, weight is measured in newtons, while it would be less on the Moon). - Mass is an intrinsic property of matter, meaning it remains constant regardless of the object's location. - Weight depends on the local gravitational field. For instance, an object weighs less on the Moon due to weaker gravity than it does on Earth.
Match the LIST-I with LIST-II
\[ \begin{array}{|l|l|} \hline \text{LIST-I} & \text{LIST-II} \\ \hline \text{A. Gravitational constant} & \text{I. } [LT^{-2}] \\ \hline \text{B. Gravitational potential energy} & \text{II. } [L^2T^{-2}] \\ \hline \text{C. Gravitational potential} & \text{III. } [ML^2T^{-2}] \\ \hline \text{D. Acceleration due to gravity} & \text{IV. } [M^{-1}L^3T^{-2}] \\ \hline \end{array} \]
Choose the correct answer from the options given below:
A small point of mass \(m\) is placed at a distance \(2R\) from the center \(O\) of a big uniform solid sphere of mass \(M\) and radius \(R\). The gravitational force on \(m\) due to \(M\) is \(F_1\). A spherical part of radius \(R/3\) is removed from the big sphere as shown in the figure, and the gravitational force on \(m\) due to the remaining part of \(M\) is found to be \(F_2\). The value of the ratio \( F_1 : F_2 \) is: 