Answer:
1000 kgm²/s, 400 J
1000 kgm²/s, 1000 J
600 J
Explanation:
m = Mass of astronauts = 100 kg
d = Diameter
r = Radius = ![\frac{d}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D)
v = Velocity of astronauts = 2 m/s
Angular momentum of the system is given by
![L=mvr+mvr\\\Rightarrow L=2mvr\\\Rightarrow L=2\times 100\times 2\times 2.5\\\Rightarrow L=1000\ kgm^2/s](https://tex.z-dn.net/?f=L%3Dmvr%2Bmvr%5C%5C%5CRightarrow%20L%3D2mvr%5C%5C%5CRightarrow%20L%3D2%5Ctimes%20100%5Ctimes%202%5Ctimes%202.5%5C%5C%5CRightarrow%20L%3D1000%5C%20kgm%5E2%2Fs)
The angular momentum of the system is 1000 kgm²/s
Rotational energy is given by
![K=I\omega^2\\\Rightarrow K=\frac{1}{2}(mr^2)\left(\frac{v}{r}\right)^2\\\Rightarrow K=mv^2\\\Rightarrow K=100\times 2^2\\\Rightarrow K=400\ J](https://tex.z-dn.net/?f=K%3DI%5Comega%5E2%5C%5C%5CRightarrow%20K%3D%5Cfrac%7B1%7D%7B2%7D%28mr%5E2%29%5Cleft%28%5Cfrac%7Bv%7D%7Br%7D%5Cright%29%5E2%5C%5C%5CRightarrow%20K%3Dmv%5E2%5C%5C%5CRightarrow%20K%3D100%5Ctimes%202%5E2%5C%5C%5CRightarrow%20K%3D400%5C%20J)
The rotational energy of the system is 400 J
There no external toque present so the initial and final angular momentum will be equal to the initial angular momentum 1000 kgm²/s
![L_i=L_f\\\Rightarrow 2mv_ir_i=2mv_fr_f\\\Rightarrow v_f=\frac{v_ir_i}{r_f}\\\Rightarrow v_f=\frac{2\times 2.5}{0.5}\\\Rightarrow v_f=10\ m/s](https://tex.z-dn.net/?f=L_i%3DL_f%5C%5C%5CRightarrow%202mv_ir_i%3D2mv_fr_f%5C%5C%5CRightarrow%20v_f%3D%5Cfrac%7Bv_ir_i%7D%7Br_f%7D%5C%5C%5CRightarrow%20v_f%3D%5Cfrac%7B2%5Ctimes%202.5%7D%7B0.5%7D%5C%5C%5CRightarrow%20v_f%3D10%5C%20m%2Fs)
Energy
![E_2=mv_f^2\\\Rightarrow E_2=100\times 10\\\Rightarrow E_2=1000\ J](https://tex.z-dn.net/?f=E_2%3Dmv_f%5E2%5C%5C%5CRightarrow%20E_2%3D100%5Ctimes%2010%5C%5C%5CRightarrow%20E_2%3D1000%5C%20J)
The new energy will be 1000 J
Work done will be the change in the kinetic energy
![W=E_2-E\\\Rightarrow W=1000-400\\\Rightarrow W=600\ J](https://tex.z-dn.net/?f=W%3DE_2-E%5C%5C%5CRightarrow%20W%3D1000-400%5C%5C%5CRightarrow%20W%3D600%5C%20J)
The work done is 600 J
Answer: A is your best answer.
Explanation:
It should be A because the when the ball bounces on the ground the ground will give it force to bounce again but also it wont go as high as it first did. Hope this helps:))
The hypothesis because its very hard to make and it confounds me
Answer:
The velocity of the other fragment immediately following the explosion is v .
Explanation:
Given :
Mass of original shell , m .
Velocity of shell , + v .
Now , the particle explodes into two half parts , i.e
.
Since , no eternal force is applied in the particle .
Therefore , its momentum will be conserved .
So , Final momentum = Initial momentum
![mv=\dfrac{mv}{2}+\dfrac{mu}{2}\\\\u=v](https://tex.z-dn.net/?f=mv%3D%5Cdfrac%7Bmv%7D%7B2%7D%2B%5Cdfrac%7Bmu%7D%7B2%7D%5C%5C%5C%5Cu%3Dv)
The velocity of the other fragment immediately following the explosion is v .