The position of an object having mass 0.1 kg as a function of time t is given as \(\vec{r}=\left(10{t}^{2}\overset{^}{i}+5{t}^{3}\overset{^}{j}\right)\). At t=1 s, which of the following statements are correct?
A. The linear momentum \(\vec{p}=(2\overset{^}{i}+1.5\overset{^}{j})kgm/s\).
B. The force acting on the object \(\vec{F}=(2\overset{^}{i}+3\overset{^}{j})N\).
C. The angular momentum of the object about its origin \(\vec{L}=15\overset{^}{k}Js\).
D. The torque acting on the object about its origin \(\vec{\tau }=20\overset{^}{k}Nm\).

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[JEE Main 2026, 2 Apr (Shift 1)]

Question

The position of an object having mass 0.1 kg as a function of time t is given as \(\vec{r}=\left(10{t}^{2}\overset{^}{i}+5{t}^{3}\overset{^}{j}\right)\). At t=1 s, which of the following statements are correct?
A. The linear momentum \(\vec{p}=(2\overset{^}{i}+1.5\overset{^}{j})kgm/s\).
B. The force acting on the object \(\vec{F}=(2\overset{^}{i}+3\overset{^}{j})N\).
C. The angular momentum of the object about its origin \(\vec{L}=15\overset{^}{k}Js\).
D. The torque acting on the object about its origin \(\vec{\tau }=20\overset{^}{k}Nm\).

Choose the correct answer from the options given below:

[JEE Main 2026, 2 Apr (Shift 1)]

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