Question 324: Centre of Mass and Rotational Motion

Question

A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is suspended from its end $$A.$$A$$ set of $$(m,x)$$ values is recorded. The appropriate variables that give a straight line, when plotted, are :

Accepted Answer

Here, let the length of the rod is = $$\ell $$ and mass = m.
In equilibrium, torque about point  of suspension x,
mg x = $$\left( {{\ell  \over 2} - x} \right)Mg$$
$$ \Rightarrow \,\,\,\,$$ mx = M$${\ell  \over 2}$$ $$-$$ mx
$$ \Rightarrow \,\,\,\,$$ m = $$\left( {{{m\ell } \over 2}} \right){1 \over x} - M$$
Comparing this straight  line equation,  y = mx + c
This is a straight line equation when we plot with variable m and $${1 \over x}$$.

Answer

$$m,x$$

Answer

$$m,{1 \over x}$$

Answer

$$m,{1 \over {{x^2}}}$$

Answer

$$m,{x^2}$$

Centre of Mass and Rotational Motion

A uniform rod $AB is suspended from a point X, at a variable distance x from A, as shown, To make the rod horizontal, a mass m is suspended from its end A.A set of (m,x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are :

Choose the correct answer: