Answer:
![=\frac{1/3}{5/6} = 0.4](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%2F3%7D%7B5%2F6%7D%20%3D%200.4)
Explanation:
Moment of inertia of given shell![= \frac{2}{3} MR^2](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20MR%5E2)
where
M represent sphere mass
R -sphere radius
we know linear speed is given as ![v = r\omega](https://tex.z-dn.net/?f=v%20%3D%20r%5Comega)
translational ![K.E = \frac{1}{2} mv^2 = \frac{1}{2} m(r\omega)^2](https://tex.z-dn.net/?f=K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%28r%5Comega%29%5E2)
rotational ![K.E = \frac{1}{2} I \omega^2 = \frac{1}{2} \frac{2}{3} MR^2 \omega^2](https://tex.z-dn.net/?f=K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20I%20%5Comega%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7B2%7D%7B3%7D%20MR%5E2%20%5Comega%5E2)
total kinetic energy will be
![K.E = \frac{1}{2} m(r\omega)^2 + \frac{1}{2} \frac{2}{3} MR^2 \omega^2](https://tex.z-dn.net/?f=K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%28r%5Comega%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7B2%7D%7B3%7D%20MR%5E2%20%5Comega%5E2)
![K.E =\frac{5}{6} MR^2 \omega^2](https://tex.z-dn.net/?f=K.E%20%3D%5Cfrac%7B5%7D%7B6%7D%20MR%5E2%20%5Comega%5E2)
fraction of rotaional to total K.E
![=\frac{1/3}{5/6} = 0.4](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%2F3%7D%7B5%2F6%7D%20%3D%200.4)
Answer: The electric repulsion between the two protons is stronger than the gravitational attraction.
Explanation: Please see the attachments below
Answer:
The tension increases to four times its original value.
Explanation:
v = Velocity
r = Radius
m = Mass of stone
The centripetal force is
![F_c=m\dfrac{v^2}{r}](https://tex.z-dn.net/?f=F_c%3Dm%5Cdfrac%7Bv%5E2%7D%7Br%7D)
The tension will balance the centripetal force
![T=m\dfrac{v^2}{r}](https://tex.z-dn.net/?f=T%3Dm%5Cdfrac%7Bv%5E2%7D%7Br%7D)
![\\\Rightarrow T\propto v^2](https://tex.z-dn.net/?f=%5C%5C%5CRightarrow%20T%5Cpropto%20v%5E2)
![\dfrac{T_1}{T_2}=\dfrac{v_1^2}{v_2^2}\\\Rightarrow \dfrac{T_1}{T_2}=\dfrac{v_1}{2^2v_1^2}\\\Rightarrow \dfrac{T_1}{T_2}=\dfrac{1}{4}\\\Rightarrow T_2=4T_1](https://tex.z-dn.net/?f=%5Cdfrac%7BT_1%7D%7BT_2%7D%3D%5Cdfrac%7Bv_1%5E2%7D%7Bv_2%5E2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7BT_1%7D%7BT_2%7D%3D%5Cdfrac%7Bv_1%7D%7B2%5E2v_1%5E2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7BT_1%7D%7BT_2%7D%3D%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5CRightarrow%20T_2%3D4T_1)
The new tension will be 4 times the old tension
the car travels 34 mi in one hour.
then, in 6 hours car travels
34 x 6 mi
= 204 mi