At time t second, a particle of mass 3 kg has position vector r → metre where r → = (3 t) i ^ - (4 cos t) j ^ . The impulse of the force during the time interval 0 ≤ t ≤ π 2 is

∵ r → = 3 t i ^ - 4 cos ⁡ t j ^ ∴ v → = d r → d t = 3 i ^ + 4 sin ⁡ t j ^ ∴ a → = d 2 r → d t 2 = 4 cos ⁡ t j ^ ∴ F → = m a → = 12 cos ⁡ t j ^ ∴ Impluse = ∫ 0 π 2 F d t = 12 ∫ 0 π 2 cos ⁡ t d t = 12 sin ⁡ t 0 π 2 = 12 N - s The direction of impulse will be in the direction of force. ∴ Impulse = 12 N - s j ^

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Physics - NLM Question with Solution | TestHub

PhysicsNLMMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

At time t second, a particle of mass 3 kg has position vector $\vec{r}$ metre where $\vec{r} = (3 t) \hat{i} - (4 \cos t) \hat{j}$ . The impulse of the force during the time interval $0 \leq t \leq \frac{π}{2}$ is

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Answer:

Solution:

$∵$ $\vec{r} = 3 t \hat{i} - 4 \cos t \hat{j}$

$∴$ $\vec{v} = \frac{d \vec{r}}{d t} = 3 \hat{i} + 4 \sin t \hat{j}$

$∴$ $\vec{a} = \frac{d^{2} \vec{r}}{d t^{2}} = 4 \cos t \hat{j}$

$∴$ $\vec{F} = m \vec{a} = 12 \cos t \hat{j}$

$∴$ Impluse $= \int_{0}^{\frac{π}{2}} F d t = 12 \int_{0}^{\frac{π}{2}} \cos t d t$

$= 12 {[\sin t]}_{0}^{\frac{π}{2}} = 12 N - s$

The direction of impulse will be in the direction of force.

$∴$ Impulse $= (12 N - s) \hat{j}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:NLMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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