Answer:
(D) 3
Explanation:
The angular momentum is given by:
![\vec{L}=\vec{r}\ X \ \vec{p}](https://tex.z-dn.net/?f=%5Cvec%7BL%7D%3D%5Cvec%7Br%7D%5C%20X%20%5C%20%5Cvec%7Bp%7D)
Thus, the magnitude of the angular momenta of both solar systems are given by:
![L_1=Rm_1v_1=Rm_1(\omega R)=R^2m_1(\frac{2\pi}{T_1})=2\pi R^2\frac{m_1}{T_1}\\\\L_2=Rm_2v_2=2\pi R^2\frac{m_2}{T_2}](https://tex.z-dn.net/?f=L_1%3DRm_1v_1%3DRm_1%28%5Comega%20R%29%3DR%5E2m_1%28%5Cfrac%7B2%5Cpi%7D%7BT_1%7D%29%3D2%5Cpi%20R%5E2%5Cfrac%7Bm_1%7D%7BT_1%7D%5C%5C%5C%5CL_2%3DRm_2v_2%3D2%5Cpi%20R%5E2%5Cfrac%7Bm_2%7D%7BT_2%7D)
where we have taken that both systems has the same radius.
By taking into account that T1=3T2, we have
![L_1=2\pi R^2\frac{m_1}{3T_2}=\frac{1}{3}2\pi R^2\frac{1}{T_2}m_1=\frac{1}{3}\frac{L_2}{m_2}m_1](https://tex.z-dn.net/?f=L_1%3D2%5Cpi%20R%5E2%5Cfrac%7Bm_1%7D%7B3T_2%7D%3D%5Cfrac%7B1%7D%7B3%7D2%5Cpi%20R%5E2%5Cfrac%7B1%7D%7BT_2%7Dm_1%3D%5Cfrac%7B1%7D%7B3%7D%5Cfrac%7BL_2%7D%7Bm_2%7Dm_1)
but L1=L2=L:
![L=\frac{1}{3}L\frac{m_1}{m_2}\\\\\frac{m_1}{m_2}=3](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B1%7D%7B3%7DL%5Cfrac%7Bm_1%7D%7Bm_2%7D%5C%5C%5C%5C%5Cfrac%7Bm_1%7D%7Bm_2%7D%3D3)
Hence, the answer is (D) 3
HOPE THIS HELPS!!
Answer:
Option B
Explanation:
Option A is the wrong answer because the horizontal vector is in the opposite direction.
Option C is the wrong answer as the horizontal vector is in the opposite direction and all the vectors are connected head to tail [of the arrows] [Triangle law of vector addition]
Option D is the wrong answer as the horizontal vector is in the opposite direction.