What is the size of mass M?

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A4: Size of mass M

Apply the principle of moments.
For the metre rule to be in equilibrium, the sum of the clockwise moments about the pivot must equal the sum of the anticlockwise moments about the pivot. The pivot is at the $50 \text{ cm}$ mark.
Calculate the anticlockwise moment.
Mass M is at the $0 \text{ cm}$ mark. Its distance from the pivot is $50 \text{ cm} - 0 \text{ cm} = 50 \text{ cm}$ .
Anticlockwise moment = $M \times 50 \text{ cm}$ .
Calculate the clockwise moment.
The $100 \text{ g}$ mass is at the $90 \text{ cm}$ mark (since it's $10 \text{ cm}$ from the $100 \text{ cm}$ end). Its distance from the pivot is $90 \text{ cm} - 50 \text{ cm} = 40 \text{ cm}$ .
Clockwise moment = $100 \text{ g} \times 40 \text{ cm}$ .
Equate the moments and solve for M.
$M \times 50 \text{ cm} = 100 \text{ g} \times 40 \text{ cm}$ $M = \frac{100 \text{ g} \times 40 \text{ cm}}{50 \text{ cm}}$ $M = \frac{4000 \text{ g}}{50}$ $M = 80 \text{ g}$
The correct option is C.
$\boxed{\text{C}}$
A5: Kinetic energy of the learner
Identify the given values.
Mass of the learner, $m = 20 \text{ kg}$
Velocity of the learner, $v = 6.0 \text{ m/s}$
Use the formula for kinetic energy.
The formula for kinetic energy (KE) is:
$KE = \frac{1}{2}mv^2$
Substitute the values and calculate the kinetic energy.
$KE = \frac{1}{2} \times 20 \text{ kg} \times (6.0 \text{ m/s})^2$ $KE = \frac{1}{2} \times 20 \text{ kg} \times 36 \text{ m}^2/\text{s}^2$ $KE = 10 \text{ kg} \times 36 \text{ m}^2/\text{s}^2$ $KE = 360 \text{ J}$
The correct option is C.
$\boxed{\text{C}}$
A6: Heat transfer to the hand
Analyze the heat transfer processes involved.
When one end of a metal rod is heated by a flame, heat travels through the solid metal rod to the hand primarily by conduction. This is the transfer of thermal energy through direct contact of particles.
Consider other possible heat transfer mechanisms.
The flame and the hot part of the metal rod also emit radiation (infrared radiation), which can travel through the air and be absorbed by the hand.
Convection involves heat transfer through the movement of fluids (like air). While the air around the rod will heat up and move, it is not the primary way heat reaches the hand through the rod.
Determine the most significant processes reaching the hand.
The heat travels along the rod to the hand by conduction. Additionally, the hand will feel heat radiated from the flame and the hot part of the rod. Therefore, both conduction and radiation contribute to the heat reaching the hand.
The correct option is C.
$\boxed{\text{C}}$

What is the size of mass M?

Answer

Step-by-step solution

Apply the principle of moments.

Calculate the anticlockwise moment.

Calculate the clockwise moment.

Equate the moments and solve for M.

Identify the given values.

Use the formula for kinetic energy.

Substitute the values and calculate the kinetic energy.

Analyze the heat transfer processes involved.

Consider other possible heat transfer mechanisms.

Determine the most significant processes reaching the hand.

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