Work Done Worksheet

**Page 1**

1.

Find the centroid of the region bounded by $y$ = $x$^{2}, 1 ≤ $x$ ≤ 2.

a. | ($\frac{45}{28}$, $\frac{93}{30}$) | ||

b. | ($\frac{45}{30}$, $\frac{93}{28}$) | ||

c. | ($\frac{45}{14}$, $\frac{93}{30}$) | ||

d. | ($\frac{45}{14}$, $\frac{93}{70}$) | ||

e. | ($\frac{45}{28}$, $\frac{93}{70}$) |

Area bounded by the curve

A =

=

are the coordinates of the centroid of the region under

=

=

Centroid of the region is (

Correct answer : (5)

2.

Find the center of mass of the point masses $m$_{1} = 6, $m$_{2} = 8 and $m$_{3} = 10, lying at $x$_{1} = - 1, $x$_{2} = 2 and $x$_{3} = 3 on the $x$-axis respectively.

a. | $\frac{13}{6}$ | ||

b. | $\frac{6}{13}$ | ||

c. | $\frac{5}{3}$ | ||

d. | $\frac{2}{3}$ | ||

e. | $\frac{3}{5}$ |

M

M

Center of mass

Correct answer : (3)

3.

Find the center of mass of the system of point masses $m$_{1} = 2, $m$_{2} = 1 and $m$_{3} = 4, lying at (1, 1), (1, - 1) and (1, 0) respectively.

a. | ($\frac{1}{7}$, $\frac{1}{7}$) | ||

b. | (1, $\frac{1}{7}$) | ||

c. | (7, 7) | ||

d. | (1, 1) | ||

e. | ($\frac{1}{7}$, 1) |

M

M

M

The center of mass of the system is (

Correct answer : (2)

4.

Find the center of mass of the wire of length 10 units lying on the interval [0, 10], if its density at the point $x$ is $x$^{2}.

a. | $\frac{3}{4}$ | ||

b. | $\frac{4}{3}$ | ||

c. | $\frac{2}{15}$ | ||

d. | $\frac{2}{5}$ | ||

e. | $\frac{15}{2}$ |

= [

=

So, the center of mass is

Correct answer : (5)

5.

The center of mass of the point masses $m$_{1} = 2, $m$_{2} = 6, $m$_{3} = m and $m$_{4} = 4, lying at $x$_{1} = - 4, $x$_{2} = - 2, $x$_{3} = - 1 and $x$_{4} = 10 respectively is 1. Find $m$.

a. | $\frac{1}{4}$ | ||

b. | $\frac{1}{2}$ | ||

c. | 1 | ||

d. | 2 | ||

e. | 4 |

Then the moment of the masses with respect to the

M

M

m =

Center of mass

20 -

Correct answer : (5)

6.

The center of mass of the system of point masses $m$_{1} = 3, $m$_{2} = 2 and $m$_{3} = $k$, lying at (2, 1), (3, 2) and (4, 5) respectively is (3, $\stackrel{\u203e}{y}$). Find $\stackrel{\u203e}{y}$.

a. | $\frac{2}{11}$ | ||

b. | $\frac{11}{2}$ | ||

c. | $\frac{4}{11}$ | ||

d. | 1 | ||

e. | $\frac{11}{4}$ |

M

M

[

M

Correct answer : (5)

7.

Find the centroid of the region bounded by $y$ = $x$, 2 ≤ $x$ ≤ 4.

a. | ($\frac{28}{9}$,$\frac{14}{9}$) | ||

b. | ($\frac{7}{9}$,$\frac{14}{9}$) | ||

c. | ($\frac{14}{9}$,$\frac{28}{9}$) | ||

d. | ($\frac{28}{9}$,$\frac{28}{9}$) | ||

e. | ($\frac{14}{9}$,$\frac{14}{9}$) |

=

[Use

[Use

So, the centroid of the region is (

Correct answer : (1)

8.

When a sugar bag is moved 10 meters with a force 100 newtons, what is the work done against resistance?

a. | 1000 newton-meters | ||

b. | 100000 newton-meters | ||

c. | 100 newton-meters | ||

d. | 10 newton-meters | ||

e. | 10000 newton-meters |

Work done = 100 × 10 = 1000 newton-meters

So, the work done against resistance is 1000 newton-meters.

Correct answer : (1)

9.

When a 20 pound disc is lifted 10 feet, what is the work done against gravity?

a. | 200 foot-pounds | ||

b. | 500 foot-pounds | ||

c. | 2000 foot-pounds | ||

d. | 100 foot-pounds | ||

e. | 1000 foot-pounds |

Work done = 20 × 10 = 200 foot-pounds

So, the work done against gravity is 200 foot-pounds.

Correct answer : (1)

10.

What is the work done, when a spring is extended 4 cm from its natural length with a force 4000 newtons?

a. | 800 newton-meters | ||

b. | 40 newton-cm | ||

c. | 4000 newton-meters | ||

d. | 400 newton-cm | ||

e. | 8000 newton-cm |

[Hooke's law.]

[Evaluation of

Work done =

[Work done =

= (

So, the work done is 8000 newton-cm.

Correct answer : (5)