Choose the correct answer from the options given below:
List – I List – II (a) Gravitational constant (i) [L2T-2] (b) Gravitational potential energy (ii) [M-1L3T-2] (c) Gravitational potential (iii) [LT-2] (d) Gravitational intensity (iv) [ML2T-2
Choose the correct answer from the options given below:
| List – I | List – II |
|---|---|
| (a) Gravitational constant | (i) [L2T-2] |
| (b) Gravitational potential energy | (ii) [M-1L3T-2] |
| (c) Gravitational potential | (iii) [LT-2] |
| (d) Gravitational intensity | (iv) [ML2T-2 |
(a) - (ii), (b) - (i), (c)-(iv), (d) - (iii)
(a) - (ii), (b) - (iv), (c)-(i), (d) - (iii)
(a) - (ii), (b) - (iv), (c)-(iii), (d) - (i)
(a) - (iv), (b) - (ii), (c)-(i), (d) - (iii)
The Correct Option is B
Solution and Explanation
To solve this problem, we need to match the physical quantities in List-I with their respective dimensional formulas in List-II. We will use our knowledge of dimensional formulas for each term:
- Gravitational constant (G): The dimensional formula for gravitational constant is:
[M-1L3T-2](ii). - Gravitational potential energy: The dimensional formula is derived from energy,
[ML2T-2](iv). - Gravitational potential: This is energy per unit mass, so the dimensional formula is:
[L2T-2](i). - Gravitational intensity: This is force per unit mass, leading to the dimensional formula:
[LT-2](iii).
This matches with the option: (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii).
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Concepts Used:
Gravitational Potential Energy
The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:
PEgrav = mass x g x height
PEgrav = m x g x h
Where,
m is the mass of the object,
h is the height of the object
g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.