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SSC Scientific Assistant Previous Paper 6 (Held On: 24 November 2017 Shift 2)

Option 3 : Gravitational potential energy

SSC IMD - Full Mock Test (CS & IT)

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__CONCEPT__:

- Dimensions: When a derived quantity is expressed in terms of fundamental quantities, it is written as a product of different powers of the fundamental quantities.
- The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.

__EXPLANATION__:

Gravitational Potential Energy (U):

- The gravitational potential energy of a body is the energy associated with it due to its position in the gravitational field of another body and is measured by the amount of work done in bringing a body from infinity to a given point in the gravitational field of the other.

- Mathematically gravitational potential energy can be written as:

⇒ U = m × g × h

As we know, the dimension of mass (m) = [M]

The dimension of acceleration due to gravity (g) is = [LT-2]

The dimension of height (h) = [L]

∴ The dimension of gravitational potential energy is

⇒ U = [M] × [LT-2] × [L]

⇒ U = [ML2T-2]

- Some Basic Dimensional formula:

Sl. No. |
Quantity |
Common Symbol |
SI Unit |
Dimension |

1 |
Velocity |
v, u |
ms-1 |
LT-1 |

2 |
Acceleration |
a |
ms-2 |
LT-2 |

3 |
Force |
F |
Newton (N) |
M L T-2 |

4 |
Momentum |
p |
Kg-ms-1 |
M L T-1 |

5 |
Gravitational constant |
G |
N-m2Kg-2 |
L3 M-1 T-2 |

6 |
Torque |
τ |
N-m |
M L2 T-2 |

7 |
Bulk Modulus |
B |
Nm2 |
M L-1 T-2 |

8 |
Energy |
E, U, K |
joule (J) |
M L2 T-2 |

9 |
Heat |
Q |
joule (J) |
M L2 T-2 |

10 |
Pressure |
P |
Nm-2 (Pa) |
M L-1 T-2 |

11 |
Electric Field |
E |
Vm-1, NC-1 |
M L I-1 T-3 |

12 |
Potential (voltage) |
V |
V, JC-1 |
M L2 I-1 T-3 |