SATHEE: Work Energy and Power - Result Question 14

Work Energy and Power - Result Question 14

16. A block of mass $10 k g$ , moving in $x$ direction with a constant speed of $10 m s^{- 1}$ , is subject to a retarding force $F = 0.1 x J / m$ during its travel from $x = 20 m$ to $30 m$ . Its final $K E$ will be:

[2015]

(a) $450 J$

(b) $275 J$

(d) $475 J$

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Answer:

Correct Answer: 16. (d)

Solution:

(d) Given, $m = 10 k g$

$u = 10 m / s e c$

Retarding force, $F = 0.1 x J / m$

Acceleration, $a = \frac{F}{m}$

$a = \frac{0.1 x}{10} = 0.01 x$

From, $v^{2} = u^{2} - 2 a s$

$\Rightarrow v^{2} = (10)^{2} - 2 \times 0.01 \int_{2} 0^{30} x d x$

$\Rightarrow v^{2} = 100 - 0.02 [\frac{x^{2}}{2}]_{2} 0^{30}$

$\Rightarrow v^{2} = 100 - \frac{0.02}{2} [(30)^{2} - (20)^{2}]$

$\Rightarrow v^{2} = 100 - 0.01 [900 - 400]$

$\Rightarrow v^{2} = 100 - 0.01 [500]$

$\Rightarrow v^{2} = 95 m / s e c$

Final K.E. $= \frac{1}{2} m v^{2}$

$= \frac{1}{2} \times 10 \times 95 \Rightarrow 475 J$

From, $F = m a$

$a = \frac{F}{m} = \frac{0.1 x}{10} = 0.01 x = V \frac{d V}{d x}$

So, $Double subscripts: use braces to clarify$

$\begin{aligned} - . \frac{V^{2}}{2} |_{V_{1}}^{V_{2}} = . \frac{x^{2}}{200} |_{20}^{30} = \frac{30 \times 30}{200} - \frac{20 \times 20}{200} \\ = 4.5 - 2 = 2.5 \\ \frac{1}{2} m (V_{2}^{2} - V_{1}^{2}) = 10 \times 2.5 J = - 25 J \end{aligned}$

Final K.E.

$\begin{aligned} = \frac{1}{2} m v_{2}^{2} = \frac{1}{2} m v_{1}^{2} - 25 = \frac{1}{2} \times 10 \times 10 \times 10 - 25 \\ = 500 - 25 = 475 J \end{aligned}$

Work Energy and Power - Result Question 14

16. A block of mass $10 k g$ , moving in $x$ direction with a constant speed of $10 m s^{- 1}$ , is subject to a retarding force $F = 0.1 x J / m$ during its travel from $x = 20 m$ to $30 m$ . Its final $K E$ will be:

Answer:

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Work Energy and Power - Result Question 14

16. A block of mass 10kg, moving in x direction with a constant speed of 10ms−1, is subject to a retarding force F=0.1xJ/m during its travel from x=20m to 30m. Its final KE 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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16. A block of mass $10 k g$ , moving in $x$ direction with a constant speed of $10 m s^{- 1}$ , is subject to a retarding force $F = 0.1 x J / m$ during its travel from $x = 20 m$ to $30 m$ . Its final $K E$ will be: