Can someone plz check if what I typed is good :)

Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bu

vlada-n [284]

Answer:

$\frac{1}{10}$ M

Explanation:

To apply the concept of angular momentum conservation, there should be no external torque before and after

As the asteroid is travelling directly towards the center of the Earth, after impact ,it does not impose any torque on earth's rotation, So angular momentum of earth is conserved

⇒ $I_{1} \times W_{1} =I_{2} \times W_{2}$

$I_{1}$ is the moment of interia of earth before impact
$W_{1}$ is the angular velocity of earth about an axis passing through the center of earth before impact
$I_{2}$ is moment of interia of earth and asteroid system
$W_{2}$ is the angular velocity of earth and asteroid system about the same axis

let $W_{1}=W$

since $\text{Time period of rotation}∝$ $\frac{1}{\text{Angular velocity}}$

⇒ if time period is to increase by 25%, which is $\frac{5}{4}$ times, the angular velocity decreases 25% which is $\frac{4}{5}$ times

therefore $W_{1}$ $=$ $\frac{4}{5} \times W_{1}$

$I_{1}=\frac{2}{5} \times M\times R^{2}$ (moment of inertia of solid sphere)

where M is mass of earth

R is radius of earth

$I_{2}=\frac{2}{5} \times M\times R^{2}+M_{1}\times R^{2}$

(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)

where $M_{1}$ is mass of asteroid

⇒ $\frac{2}{5} \times M\times R^{2} \times W_{1}=}(\frac{2}{5} \times M\times R^{2}$ $+$ $M_{1}\times R^{2})\times(\frac{4}{5} \times W_{1})$

$\frac{1}{2} \times M\times R^{2}$ = $(\frac{2}{5} \times M\times R^{2}$ + $M_{1}\times R^{2})$

$M_{1}\times R^{2}=$ $\frac{1}{10} \times M\times R^{2}$

⇒ $M_{1}=}$ $\frac{1}{10} \times M$

3 0

3 years ago

find the distance traveled in km when the average speed is 60 km per hour and the time taken is 3 and 1/2 hours

Anna35 [415]

Answer:

210 km

Explanation:

60 x 3 1/2 = 210

3 0

3 years ago

On earth which of the following are being investigated to contain fusion reactions

Vera_Pavlovna [14]

Answer:

A. Inertial Confinement and B. Magnetic Confinement

3 0

3 years ago

Read 2 more answers

What is fire department of the day

Andrej [43]

Fire Service Day
International Firefighters' Day (IFFD) is observed on May 4. It was instituted after a proposal was emailed out across the world on January 4, 1999 due to the deaths of five firefighters in tragic circumstances in a bushfire in Australia.

5 0

3 years ago

Read 2 more answers

An internal combustion engine uses fuel, of energy content 44.4 MJ/kg, at a rate of 5 kg/h. If the efficiency is 28%, determine

Alika [10]

Efficiency = Power Output / Power Input

Power Input = Rate of Energy input = 44.4 MJ/kg * 5 kg/h

= 222 MJ/h

But 1 hour = 3600seconds

222 MJ/h = 222 MJ/3600s = 0.061667 MW J/s = Watts

Power input = 0.061667 MW = 61 667 W

From Efficiency = Power Output / Power Input

   28% = Power Output / 61667

   Power Output = 0.28 * 61667

   Power Output = 17266.76 W

    Power Output ≈ 17 267 W

   Rate of heat rejection = Power Input - Power Output

   = 61667 - 17267 = 44400 W

   Rate of heat rejection = 44 400W.

8 0

3 years ago