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The dimensional formula of polarisation (electric dipole moment per unit volume) is:
Electric polarisation $P = \dfrac{\text{dipole moment}}{\text{volume}}$
Electric dipole moment $p = q \cdot d$, so $[p] = C \cdot L = A \cdot T \cdot L$
$[P] = \dfrac{[p]}{[V]} = \dfrac{ATL}{L^3} = ATL^{-2} = L^{-2}T^1A^1$
The displacement of a particle is given by $s = t^3 - 6t^2 + 3t + 4$ metres. The velocity when acceleration is zero is:
$v = \dfrac{ds}{dt} = 3t^2 - 12t + 3$
$a = \dfrac{dv}{dt} = 6t - 12$
Setting $a = 0$: $t = 2\text{ s}$
$v\big|_{t=2} = 3(4) - 12(2) + 3 = 12 - 24 + 3 = \mathbf{-9\text{ m/s}}$
A firm maintains an allowance for doubtful debts at 5% of trade receivables. This year, trade receivables were $8,000, which represented a 20% decrease from the previous year. How will this change affect the current year's profit?
1. Current Receivables = $8,000. Current Allowance = $8,000 $\times$ 5% = $400.
2. Last Year Receivables = $8,000 / 0.80 = $10,000. Last Year Allowance = $10,000 $\times$ 5% = $500.
3. Change = $500 - $400 = $100 reduction in allowance.
A reduction in allowance is credited to the income statement, thus increasing profit by $100.
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