The new oscillation frequency of the pendulum clock is 1.14 rad/s.
The given parameters;
- <em>Mass of the pendulum, = M </em>
- <em>Length of the pendulum, = L</em>
- <em>Initial angular speed, </em>
<em> = 1 rad/s</em>
The moment of inertia of the rod about the end is given as;
The moment of inertia of the rod between the middle and the end is calculated as;
![I_f = \int\limits^L_{L/2} {r^2\frac{M}{L} } \, dr = \frac{M}{3L} [r^3]^L_{L/2} = \frac{M}{3L} [L^3 - \frac{L^3}{8} ] = \frac{M}{3L} [\frac{7L^3}{8} ]= \frac{7ML^2}{24}](https://tex.z-dn.net/?f=I_f%20%3D%20%5Cint%5Climits%5EL_%7BL%2F2%7D%20%7Br%5E2%5Cfrac%7BM%7D%7BL%7D%20%7D%20%5C%2C%20dr%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5Br%5E3%5D%5EL_%7BL%2F2%7D%20%3D%20%20%5Cfrac%7BM%7D%7B3L%7D%20%5BL%5E3%20-%20%5Cfrac%7BL%5E3%7D%7B8%7D%20%5D%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5B%5Cfrac%7B7L%5E3%7D%7B8%7D%20%5D%3D%20%5Cfrac%7B7ML%5E2%7D%7B24%7D)
Apply the principle of conservation of angular momentum as shown below;
Thus, the new oscillation frequency of the pendulum clock is 1.14 rad/s.
Learn more about moment of inertia of uniform rod here: brainly.com/question/15648129
Answer:
The 50-W bulb glows more brightly than the 100-W bulb
Explanation:
The bulb has a rating of 100 W under 110 V . So it will glow with full brightness when it is fed 110 V . When bulbs are in parallel combination , each bulb receives 110 V . So they glow with full brightness .
When they are in series combination , 110 supply voltage gets distributed between the , thus , reducing the voltage appearing on each of them less than 110 V . So their brightness is reduced.
resistance = V
Bulb having high wattage rating has low resistance resulting in higher current . In the second case , both have same current as they are in series combination . So more heat will be generated in bulb having more resistance . Since 50 W bulb has higher resistance , it will glow brighter than 100 W bulb.
I think it does matter because when the pillow is in contact to the cabin it is also at a velocity of 600 km/h, but as soon as it leaves the contact of the cabin, inertia tries to slow it down and the passenger being at 600 km/h has a risk of getting hit by it.
