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Using the Principle of Calorimetry: Heat lost by metal = Heat gained by (water + calorimeter).
$m_m s_m (100 - 21.5) = (m_w s_w + m_c s_c) (21.5 - 8.4)$
$0.192 \times s_m \times 78.5 = (0.24 \times 4184 + 0.128 \times 394) \times 13.1$
$15.072 s_m = (1004.16 + 50.432) \times 13.1 = 1054.592 \times 13.1 = 13815.15$
$s_m \approx 916.6 \text{ J kg}^{-1}\text{K}^{-1}$
How many integers greater than $6000$ can be formed using the digits $3, 5, 6, 7, 8$ without repeating any digit?
Numbers greater than 6000 can be 4-digit or 5-digit.
5-digit numbers: All arrangements of 5 digits $= 5! = 120$.
4-digit numbers $> 6000$: The leading digit must be $6, 7,$ or $8$ (3 choices). Remaining 3 positions filled from 4 remaining digits: $3 \times 4 \times 3 \times 2 = 72$.
Total $= 120 + 72 = \mathbf{192}$
Centripetal force $F = \frac{mv^2}{R} \propto \frac{1}{R^n}$.
- $v^2 \propto \frac{1}{R^{n-1}} \implies v \propto R^{(1-n)/2}$
- $T = \frac{2\pi R}{v} \propto \frac{R}{R^{(1-n)/2}} = R^{1 - (\frac{1-n}{2})} = R^{(n+1)/2}$.
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