Question

A small small aluminium box has a mass of 25g and volume 520cm cube . The box is places on the surface of water. some nails are gently dropped in the box. If the mass of one nail is 3g.then how many nails can be added to the box before it sinks.

Answer 1

Answer:

165 Nails can be added

Explanation:

If an object has a higher density than the liquid it is in , it will sink

Let say n Nails are added then

Total weight of Aluminum box = 25 + 3n  gm

Volume of Aluminum box = 520 cm³

Aluminum box Density = (25 + 3n)/520  gm /cm³

Water density = 1 gm /cm³

(25 + 3n)/520 ≤ 1

=> 25 + 3n ≤ 520

=> 3n ≤ 495

=> n ≤ 165

165 Nails can be added

Answer 2

Given :

• Mass of box = 25 g
• Vol of box = 520 cm³
• Mass of nail = 3 g
• warer density = 1 g/cm³

If box has more density than water then it will sink into water

$\boxed{\bf \green{ density = \frac{mass}{vol}} } \\ \\ \Longrightarrow \bf\frac{25 + 3n}{520} \leqslant 1$

$\Longrightarrow \bf25 + 3n \leqslant 520 \\ \\ \Longrightarrow \bf 3n \leqslant 495 \\ \\\Longrightarrow \bf n \leqslant \frac{495}{3} \\ \\ \large \boxed{ \bf \orange{n = 165}}$

165 nails can added before it sink