NCERT Solutions

We need to identify the only vector quantity from the provided list of physical quantities.

Concept: Vector Quantity

A scalar quantity is a physical quantity that is completely described by its magnitude alone. In contrast, a vector quantity requires both magnitude and a specific direction in space for its complete description. Impulse ($\vec{J}$) is defined as the integral of a force ($\vec{F}$) over a time interval ($dt$):

$$\vec{J} = \int \vec{F} \, dt = \Delta \vec{p}$$

where $\vec{p}$ is the linear momentum.

Given:

The list of physical quantities is:

• Temperature
• Pressure
• Impulse
• Time
• Power
• Total path length
• Energy
• Gravitational potential
• Coefficient of friction
• Charge

Solving:

1. Scalar Quantities Analysis:

   • Temperature, time, power, energy, gravitational potential, and charge are all defined by magnitude and do not possess a spatial direction.
   • Total path length is the distance traveled along a trajectory; unlike displacement, it is a scalar.
   • The coefficient of friction is a dimensionless ratio of the magnitudes of the frictional force and the normal force, making it a scalar.
   • Pressure is defined as the magnitude of the normal force per unit area. In a fluid at rest, pressure acts equally in all directions at a point, thus it is a scalar.

2. Vector Quantity Analysis:

   • Impulse is the product of a vector (force) and a scalar (time), or equivalently, the change in a vector quantity (momentum).
   • Because it is derived from the force vector, impulse must have the same direction as the average force applied.

3. Conclusion:

   • Among the listed items, only impulse satisfies the requirement of having both magnitude and direction.

Answer:

$$\text{Impulse}$$