kg m/sec is the unit of
Impulse
This question asks us to identify the physical quantity whose unit is given as 'kg m/sec'. Let's analyze the unit and the options provided.
Unit Analysis: kg m/sec
The unit '$kg \ m/sec$' is a combination of mass (kg) and velocity (m/sec). In physics, the product of mass and velocity is known as momentum.
- Mass ($m$) has units of kilograms ($kg$).
- Velocity ($v$) has units of meters per second ($m/sec$).
- Therefore, the unit for momentum ($p = m \times v$) is '$kg \ m/sec$'.
Impulse is defined as the change in momentum, or the product of force and the time interval over which the force acts. Let's look at the units for both definitions:
- Change in momentum: As established, momentum's unit is '$kg \ m/sec$'. Therefore, the change in momentum also has units of '$kg \ m/sec$'.
- Force $\times$ Time: Force ($F$) has units of Newtons ($N$). A Newton is defined as $kg \cdot m/sec^2$. So, the unit of Force $\times$ Time is $N \times sec = (kg \cdot m/sec^2) \times sec = kg \ m/sec$.
Both definitions confirm that '$kg \ m/sec$' is the unit of impulse and momentum.
Evaluating Option Units
Let's examine the units of the other options to confirm why they are incorrect.
1. Impulse:As discussed above, the unit of impulse is '$kg \ m/sec$'. This matches the unit given in the question.
2. Angular acceleration:Angular acceleration ($\alpha$) is the rate of change of angular velocity. Its standard unit is radians per second squared ($rad/sec^2$). This does not match '$kg \ m/sec$'.
3. Capacity of condenser:The capacity of a condenser refers to capacitance ($C$). Capacitance is measured in Farads ($F$). This unit is related to charge and voltage, not mass and velocity. It does not match '$kg \ m/sec$'.
4. Acceleration:Acceleration ($a$) is the rate of change of velocity. Its standard unit is meters per second squared ($m/sec^2$). This unit involves '$sec^2$' in the denominator, unlike the given unit '$kg \ m/sec$'.
Comparison Summary
Here's a summary table comparing the units:
| Physical Quantity | Standard Unit | Does it match '$kg \ m/sec$'? |
|---|---|---|
| Impulse | $kg \ m/sec$ | Yes |
| Angular acceleration | $rad/sec^2$ | No |
| Capacity of condenser | $F$ (Farad) | No |
| Acceleration | $m/sec^2$ | No |
Conclusion
Based on the unit analysis, the unit '$kg \ m/sec$' directly corresponds to the physical quantity of Impulse (and Momentum).
Important Questions from Units, Dimensions and Measurements
According to Newton's second law of motion, force ($F$) is defined as the product of mass ($m$) and acceleration ($a$), i.e., $F=ma$. If an object with a mass of $1 \text{ kg}$ experiences an acceleration of $1 \text{ m/s}^2$, what is the standard SI unit used to quantify this force?
The standard unit of force (SI) is ____.
Which of the following instruments is used to measure the radius of wires?
The dimension of linear momentum is identical to that of which of the following expressions?
Power is defined as the rate at which energy is expended or transferred. If the dimensional formula for energy is $ML^2T^{-2}$, what is the dimensional formula of power?
