Study questions platform-wide or filter by specific tests with correct answers revealed.
A stone falls freely from rest. The distance covered in the last second of motion equals the distance covered in the first 3 seconds. How long does the stone take to reach the ground?
Distance in first 3 s: $s_3 = \dfrac{1}{2}(10)(3)^2 = 45\text{ m}$
Distance in last 1 s of total time $T$ (using $s_n = u + \dfrac{a}{2}(2n-1)$ with $u=0$):
$s_{\text{last}} = \dfrac{g}{2}(2T-1) = 5(2T-1)$
Setting equal: $5(2T-1) = 45 \Rightarrow 2T-1 = 9 \Rightarrow T = \mathbf{5\text{ s}}$
From the definition of Bulk Modulus $K$:
$\frac{\Delta V}{V} = \frac{P}{K}$ (Volume strain due to pressure)
From thermal expansion, the increase in volume is:
$\frac{\Delta V}{V} = \gamma \Delta T = 3\alpha \Delta T$
To restore the original size, the thermal expansion must equal the pressure compression:
$3\alpha \Delta T = \frac{P}{K} \implies \Delta T = \frac{P}{3\alpha K}$
Sign in to join the conversation and share your thoughts.
Log In to Comment