Question
Check true or false
(i) Work done by a conservative force in a cycle is always zero.
(ii) î x î = 0
(iii) Random motion of a gas molecules is due to heat energy.
(ix) Friction always acts as an opposing force.
(i) Work done by a conservative force in a cycle is always zero.
(ii) î x î = 0
(iii) Random motion of a gas molecules is due to heat energy.
(ix) Friction always acts as an opposing force.
Answers
GPT-4o mini
Let's evaluate each statement one by one:
(i) **Work done by a conservative force in a cycle is always zero.**
- **True.** A conservative force is defined such that the work done by the force on an object moving through a closed path (cycle) is zero. This is because the work done depends only on the initial and final positions, and in a closed cycle, those positions are the same.
(ii) **î x î = 0**
- **True.** The cross product of any vector with itself is always zero. Since î is the unit vector in the x-direction, î x î = 0.
(iii) **Random motion of gas molecules is due to heat energy.**
- **True.** The random motion of gas molecules is a result of kinetic energy, which is proportionate to the temperature (or heat energy) of the gas. As the temperature increases, so does the kinetic energy, leading to more vigorous motion.
(iv) **Friction always acts as an opposing force.**
- **True.** Friction always acts in the direction opposite to the motion or attempted motion of an object. It resists the relative motion between two surfaces in contact.
In summary:
(i) True
(ii) True
(iii) True
(iv) True
(i) **Work done by a conservative force in a cycle is always zero.**
- **True.** A conservative force is defined such that the work done by the force on an object moving through a closed path (cycle) is zero. This is because the work done depends only on the initial and final positions, and in a closed cycle, those positions are the same.
(ii) **î x î = 0**
- **True.** The cross product of any vector with itself is always zero. Since î is the unit vector in the x-direction, î x î = 0.
(iii) **Random motion of gas molecules is due to heat energy.**
- **True.** The random motion of gas molecules is a result of kinetic energy, which is proportionate to the temperature (or heat energy) of the gas. As the temperature increases, so does the kinetic energy, leading to more vigorous motion.
(iv) **Friction always acts as an opposing force.**
- **True.** Friction always acts in the direction opposite to the motion or attempted motion of an object. It resists the relative motion between two surfaces in contact.
In summary:
(i) True
(ii) True
(iii) True
(iv) True