The position of an object having mass $0.1$ kg as a function of time $t$ is given as
$\vec r=\left(10t^2\hat i+5t^3\hat j\right)$ m. At $t=1$ s, which of the following statements are **correct**?
A. The linear momentum $\vec p=\left(2\hat i+1.5\hat j\right)$ kg·m/s.
B. The force acting on the object $\vec F=\left(2\hat i+3\hat j\right)$ N.
C. The angular momentum of the object about its origin $\vec L=15\hat k$ J·s.
D. The torque acting on the object about its origin $\vec\tau=20\hat k$ N·m.
Choose the **correct** answer from the options given below:
Answer: (D) A, B and D only
At $t=1$ s: $\vec r=10\hat i+5\hat j$, $\vec v=20t\hat i+15t^2\hat j=20\hat i+15\hat j$, $\vec a=20\hat i+30t\hat j=20\hat i+30\hat j$.
A: $\vec p=m\vec v=2\hat i+1.5\hat j$ ✓
B: $\vec F=m\vec a=2\hat i+3\hat j$ ✓
C: $\vec L=\vec r\times\vec p=(10)(1.5)-(5)(2)=5\ \hat k$, not $15\hat k$ ✗
D: $\vec\tau=\vec r\times\vec F=(10)(3)-(5)(2)=20\ \hat k$ ✓
So A, B and D only.
Solution by Sreeraj P, M.Sc Physics