A metal block has the dimensions 10 cm × 5 cm × 2 cm and the density

1.	A metal block has the dimensions 10 cm × 5 cm × 2 cm and the density of the metal is 8 × 103 kg/m3. It is kept on a table with the face 10 cm × 5 cm in contact with the table. Find the force and pressure exerted by the block on the table. (g = 9.8 m/s2 )
Answer» Data : 1 = 10 cm, b = 5 cm, h = 2 cm, p= 8 × 10 kg/m³, g = 9.8 m/s² , A = lb = 10cm × 5cm = 50cm² = 50 × 104m² = 5 × 10^-5 m² , force =?, pressure = ? Volume of the block = lbh = 10 cm × 5 cm × 2 cm = 100 cm³ = 100 × 10^-6 m³ = 1 × 10^-4 m³ Mass of the block = volume × density (∵ density = mass/volume) ∴Mass of the block, m = 1 × 10^-4 m³ × 8 × 10³ kg/m³ = 0.8 kg Weight of the block = mg = 0.8 kg × 9.8 m/s² = 7.84 N ∴ The force exerted by the block on the table = 7.84 N. force 7.84 N Pressure = \(\cfrac{force}{area}\) = \(\cfrac{7.84N}{5\times10^{-3}\,m^2}\) = 1.568 × 10³ N/m² or 1.568 × 10³ Pa The pressure exerted by the block on the table = 1.568 × 10 N/m² or 1.568 × 10³ Pa.

A metal block has the dimensions 10 cm × 5 cm × 2 cm and the density of the metal is 8 × 103 kg/m3. It is kept on a table with the face 10 cm × 5 cm in contact with the table. Find the force and pressure exerted by the block on the table. (g = 9.8 m/s2 )

Answer»

Data : 1 = 10 cm, b = 5 cm,

h = 2 cm, p= 8 × 10 kg/m³, g = 9.8 m/s² ,

A = lb = 10cm × 5cm = 50cm² = 50 × 104m²

= 5 × 10^-5 m² , force =?, pressure = ?

Volume of the block = lbh = 10 cm × 5 cm × 2 cm

= 100 cm³ = 100 × 10^-6 m³ = 1 × 10^-4 m³

Mass of the block = volume × density

(∵ density = mass/volume)

∴Mass of the block,

m = 1 × 10^-4 m³ × 8 × 10³ kg/m³ = 0.8 kg

Weight of the block = mg = 0.8 kg × 9.8 m/s² = 7.84 N

∴ The force exerted by the block on the table = 7.84 N.

force 7.84 N

Pressure = \(\cfrac{force}{area}\) = \(\cfrac{7.84N}{5\times10^{-3}\,m^2}\)

= 1.568 × 10³ N/m² or 1.568 × 10³ Pa

The pressure exerted by the block on the table

= 1.568 × 10 N/m² or 1.568 × 10³ Pa.