Question

Which of the following statements are correct?
$1.$ Centre of mass of a body always coincides wiith the centre of gravity of the body.
$2.$ Centre of gravity of a body is the point where total gravitational torque on the body is zero.
$3.$ A couple on a body produces both translational and rotational motion in a body.
$4.$ Mechanical advantage greater than one means that a small effort can be used to lift a large load.

• A. $\left(1\right)$ and $\left(2\right)$
  
• B. $\left(2\right)$ and $\left(3\right)$
  
• C. $\left(3\right)$ and $\left(4\right)$
  
• D. $\left(2\right)$ and $\left(4\right)$
  

Answer 1

The correct option is D $\left(2\right)$ and $\left(4\right)$


$\Rightarrow$Force due to gravity always acts at centre of gravity, hence the torque of gravitational force about centre of gravity will be $\text{zero}$, since $mg$ will pass through this point and ${\tau }_{mg}=0$

$\Rightarrow \text{Mechanical advantage}=\frac{\text{Output force}}{\text{Input force}}$
$\therefore M.A>1\Rightarrow$ $F_{output}>F_{input}$
hence larger load can be lifted by applying smaller force.

$\Rightarrow$In a couple two equal and opposite forces acts, hence $F_{net}=0$ but ${\tau }_{net}\ne 0$ for a couple. So, rotational motion is produced in case of couple.


$\Rightarrow$Centre of mass and centre of gravity coincides only in case of symmetrical objects.
$\therefore$ Option $\left(d\right)$ is correct.