SATHEE: Centre of Mass 4 Question 4

Centre of Mass 4 Question 4

5. A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m = 0.4 k g$ is at rest on this surface. An impulse of $1.0 N s$ is applied to the block at time $t = 0$ , so that it starts moving along the $X$ -axis with a velocity $v (t) = v_{0} e^{- t / τ}$ , where $v_{0}$ is a constant and $τ = 4 s$ . The displacement of the block, in metres, at $t = τ$ is

(Take, $e^{- 1} = 0.37$ ).

(2018 Adv.)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 5. $(6.30)$

Solution:

Linear impulse, $J = m v_{0}$

$\begin{array}{ll} ∴ & v_{0} = \frac{J}{m} = 2.5 m / s \\ ∴ & v = v_{0} e^{- t / τ} \end{array}$

$\frac{d x}{d t} = v_{0} e^{- t / τ} \int_{0}^{x} d x = v_{0} \int_{0}^{τ} e^{- t / τ} d t$

$τ$

$\begin{aligned} x & = v_{0} \frac{e^{- t / τ}}{- \frac{1}{τ}} \\ x & = 2.5 (- 4) (e^{- 1} - e^{0}) \\ = 2.5 (- 4) (0.37 - 1) \\ x & = 6.30 m \end{aligned}$

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Centre of Mass 4 Question 4

Analytical & Descriptive Questions

Answer:

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