A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10, g are put

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

medium

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $10\, g$ are put one on the top of the other at the $10.0\, cm$ mark the scale is found to be balanced at $40.0\, cm$ mark. The mass of the metre scale is found to be $x \times 10^{-2}$ $kg$. The value of $x$ is

A

$9$

B

$6$

C

$60$

D

$7$

(JEE MAIN-2022)

Solution

Let mass of meter scale be $m$.

Balancing torque about knife edge

$(0.02 \;g ) \times\left(30 \times 10^{-2}\right)= mg \times\left(10 \times 10^{-2}\right)$

$m =0.06\; kg =6 \times 10^{-2} \;kg$

Standard 11

Physics

Share

Similar Questions

A uniform meter scale is supported from its $20\ cm$ mark. A body suspended from $10\ cm$ mark keeps the scale horizontal. However, the scale gets unbalanced if the body is completely immersed in water. To regain the balance the body is shifted to the $8\ cm$ mark. Therefore, the specific gravity of the material of the body is

hard

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. …….. $m$

medium

$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :

hard

A uniform meter scale balances at the $40\,cm$ mark when weights of $10\,g$ and $20\,g$ are suspended from the $10\,cm$ and $20\,cm$ marks. The weight of the metre scale is …… $g$

medium

A mass $M= 40\ kg$ is fixed at the very edge of a long plank of mass $80\ kg$ and length $1\ m$ which is pivoted such that it is in equilibrium. How far (approx.) from the pivot should a mass of $100\ kg$ be attached so that the plank starts rotating with an angular acceleration of $1\ rad/s^2$?

hard