JEE Mains · Physics · STD 11 - 4.1 newtons laws of motion
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 :
- A A, B and C only
- B B, C and D only
- C A, C and D only
- D A, B and D only
Answer & Solution
Correct Answer
(D) A, B and D only
Step-by-step Solution
Detailed explanation
Given the position vector \(\vec{r} = 10t^2\hat{i} + 5t^3\hat{j}\) Velocity \(\vec{v} = \dfrac{d\vec{r}}{dt} = 20t\hat{i} + 15t^2\hat{j}\) Acceleration \(\vec{a} = \dfrac{d\vec{v}}{dt} = 20\hat{i} + 30t\hat{j}\) At \(t = 1\) s: \(\vec{r} = 10\hat{i} + 5\hat{j}\) m…
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