Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 4

If $x\propto yz \text{and} y\propto zx$ then

If $x\propto yz, y\propto a{b}^2 \text{and} z\propto \frac{b}{a}$, then

If $x\propto \frac{1}{\sqrt{y}}$ then

If $x\propto z, y\propto \frac{1}{z}$ then

If $x\propto y, y\propto z, z\propto x$ and the constants of variation are $k, l, m$ then

$P\propto \frac{1}{V}$ when $T$ is constant and $P\propto T$ when $V$ constant and $P=R$ when $V=T$, then which of the following relations is correct?

The time period of a simple pendulum varies directly as the square root of its length. If the time period is $\mathrm{T}$ when the length is $l$, then find the time period when the length is $4l$.

If $x\propto \frac{1}{z}$ when $y$ is constant and $x\propto y$ when $z$ is constant, then when $y \text{and} z$ both vary then