Question

A metal ball immersed in water weighs w₁ at 0°C and w₂ at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then ______.

Options

• `w_1 > w_2`

• `w_1 < w_2`

• `w_1 = w_2`

• data is insufficient.

Answer 1

A metal ball immersed in water weighs w₁ at 0°C and w₂ at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then `underlinebb(w_1 < w_2)`.

Explanation:

Apparent weight `(w_a)`

= actual weight (w) – upthrust (F)

Here, F = `Vrhowg` (ρw = density of water)

i.e., `F_{0^circC} = V_{0^circC}(rhow)_{0^circC}g`

and `F_{50^circC} = V_{50^circC}(rhow)_{50^circC}g`

∴ `(F_{50^circC})/(F_{0^circC}) = (V_{50^circC})/(V_{0^circC}).((rho_w)_{50^circC})/((rho_w)_{0^circC})`

= `((1 + γ_mDeltatheta))/((1 + γ_wDeltatheta)`

(Δθ = 50°C)

Given that γm < γw

`therefore F_{50°C} < F_{0°C}`

or apparent weight at 50°C will be more.