Laws of Motion

B.

Up the incline, while ascending as well as descending

It is obvious that during ascending, a retarding i.e. anticlockwise moment is required. I should be remembered that torque due to friction has the same sense the angular acceleration.

B.

$\mathrm{\mu g} (\mathrm{towards} \mathrm{right}), \mathrm{\mu g} (\mathrm{towards} \mathrm{left})$

The force causing the motion of A is a frictional force between A and B,

So, acceleration of A

$$\begin{gathered} {\mathrm{\mu M}}_{\mathrm{B}} \mathrm{g} = {\mathrm{M}}_{\mathrm{A}}{\mathrm{a}}_{\mathrm{A}} \\ \Rightarrow {\mathrm{a}}_{\mathrm{A}} = \mathrm{\mu } \left(\frac{{\mathrm{M}}_{\mathrm{B}}}{{\mathrm{M}}_{\mathrm{A}}}\right) \mathrm{g} = \frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{right}) \end{gathered}$$

Block B experiences frictions force towards the left.

MBaB = μMBg ⇒a_B = μg towards left

Hooked law states that for a small force, Stress is directly proportional to strain. the constant of proportionality is the modulus of elasticity

Boyle’s law is a gas law which states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. Boyle’s law was put forward by the Anglo-Irish chemist Robert Boyle in the year 1662.

For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed mathematically as follows.

P ∝ (1/V)

Where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant, k.

P = k*(1/V) ⇒ PV = k

The pressure v/s volume curve for a fixed amount of gas kept at constant temperature is illustrated below.

It can be observed that a straight line is obtained when the pressure exerted by the gas (P) is taken on the Y-axis and the inverse of the volume occupied by the gas (1/V) is taken on the X-axis.