SATHEE: Work Power and Energy 5 Question 1

Work Power and Energy 5 Question 1

3. A body of mass $m = 10^{- 2} k g$ is moving in a medium and experiences a frictional force $F = - k v^{2}$ . Its initial speed is $v_{0} = 10 m s^{- 1}$ . If, after $10 s$ , its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of $k$ will be

(2017 Main)

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Answer:

Correct Answer: 3. (b)

Solution:

Given, force, $F = - k v^{2}$

$∴$ Acceleration, $a = \frac{- k}{m} v^{2}$

$\begin{aligned} or & \frac{d v}{d t} & = \frac{- k}{m} v^{2} \\ \Rightarrow & \frac{d v}{v^{2}} & = - \frac{k}{m} \cdot d t \end{aligned}$

Now, with limits, we have

$\begin{aligned} \int_{10}^{v} \frac{d v}{v^{2}} = - \frac{k}{m} \int_{0}^{t} d t \\ \Rightarrow - {\frac{1}{v}}_{10}^{v} = - \frac{k}{m} t \\ \Rightarrow \frac{1}{v} = 0.1 + \frac{k t}{m} \\ \Rightarrow v = \frac{1}{0.1 + \frac{k t}{m}} = \frac{1}{0.1 + 1000 k} \\ \Rightarrow \frac{1}{2} \times m \times v^{2} = \frac{1}{8} \times v_{0}^{2} \\ \Rightarrow v = \frac{v_{0}}{2} = 5 \\ \Rightarrow \frac{1}{0.1 + 1000 k} = 5 \\ \Rightarrow 1 = 0.5 + 5000 k \\ \Rightarrow k = \frac{0.5}{5000} \Rightarrow k = 10^{- 4} k g / m \end{aligned}$

Work Power and Energy 5 Question 1

3. A body of mass $m = 10^{- 2} k g$ is moving in a medium and experiences a frictional force $F = - k v^{2}$ . Its initial speed is $v_{0} = 10 m s^{- 1}$ . If, after $10 s$ , its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of $k$ will be

Answer:

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Work Power and Energy 5 Question 1

3. A body of mass m=10−2kg is moving in a medium and experiences a frictional force F=−kv2. Its initial speed is v0=10ms−1. If, after 10s, its energy is 18mv02, the value of k will be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. A body of mass $m = 10^{- 2} k g$ is moving in a medium and experiences a frictional force $F = - k v^{2}$ . Its initial speed is $v_{0} = 10 m s^{- 1}$ . If, after $10 s$ , its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of $k$ will be