Question Number 210912 by Tawa11 last updated on 21/Aug/24
A uniform stick AB of length L and mass M is balanced horizontally on a knife edge 10.0cm from A when an object of mass 400g is suspended at A. When the knife edge is moved 5cm further, the object has to be moved to a point 9.00cm from A for the stick to balance. Represent the balance system with a suitable diagram, determine the mass and Length of the stick
Answered by Tawa11 last updated on 21/Aug/24
Answered by mr W last updated on 21/Aug/24
Commented by mr W last updated on 21/Aug/24
$$\mathrm{400}×\mathrm{10}={M}×\left(\frac{{L}}{\mathrm{2}}−\mathrm{10}\right)\:\:\:\:...\left({i}\right) \\ $$$$\mathrm{400}×\left(\mathrm{15}−\mathrm{9}\right)={M}×\left(\frac{{L}}{\mathrm{2}}−\mathrm{15}\right)\:\:\:...\left({ii}\right) \\ $$$$\left({i}\right)/\left({ii}\right): \\ $$$$\frac{\mathrm{10}}{\mathrm{6}}=\frac{\frac{{L}}{\mathrm{2}}−\mathrm{10}}{\frac{{L}}{\mathrm{2}}−\mathrm{15}} \\ $$$$\Rightarrow{L}=\mathrm{45}\:{cm} \\ $$$$\mathrm{400}×\mathrm{10}={M}×\left(\frac{\mathrm{45}}{\mathrm{2}}−\mathrm{10}\right) \\ $$$$\Rightarrow{M}=\mathrm{320}\:{g} \\ $$
Commented by Tawa11 last updated on 21/Aug/24
$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$$$\mathrm{I}\:\mathrm{understand}\:\mathrm{very}\:\mathrm{well}\:\mathrm{now}. \\ $$