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4 years ago

Which data set has the smallest standard deviation?

2 answers:

8 0

The answer would be B.
<span>
Standard deviation basically measures how spread out the values are. Without solving, you can easily tell which one among your choices have a smaller deviation. The closer the values are to each other the smaller the standard deviation. The values of choice B are the closest together, so you can assume that they have the smallest standard deviation. </span>

lubasha [3.4K]4 years ago

7 0

Answer:

(B)1000, 1001, 1002, 1000, 1001, 1001

Explanation:

Standard deviation helps in measuring how spread out the values actually are. Without solving for the standard deviation, the smallest standard deviation of the given data sets can be easily guessed.

The closer the values are to each other, the smaller is the standard deviation. From the given data sets, The values of choice B that are 1000, 1001, 1002, 1000, 1001, 1001 are the closest together and in rest of the options the data sets hare not close to each other, so one can assume that they have the smallest standard deviation.

Hence, option B is correct.

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13. If you shorten the length of string by half that holds an object in rotation at the same tangential

Dmitrij [34]

13. doubles

The tension in the string corresponds to the centripetal force that holds the object in rotation, so:

$T=F=m\frac{v^2}{r}$

where m is the mass of the object, v is the tangential speed, and r is the distance of the object from the centre of rotation (therefore it corresponds to the length of the string). The problem tells us that the tangential speed remains the same (v), while the length of the string is halved, so r'=r/2. Therefore, the new tension in the string will be

$T'=m\frac{v^2}{r'}=m\frac{v^2}{r/2}=2m\frac{v^2}{r}=2T$

so, the Tension doubles.

14. Variations of centripetal forces

Both revolution and rotation refer to the rotational motion of an object, therefore they both involve the presence of a centripetal force, which keeps the object in circular motion. The only difference between the two is:

- Revolution is the circular motion of an object around a point external to the object (for instance, the motion of the Earth around the Sun)

- Rotation is the circular motion of an object around its centre, so around a point internal to the object (for instance, the rotation of the Earth around its axis)

15. Rotational speed

For a uniform object in circular motion, all the points of the object have same rotational speed. In fact, the rotational speed is defined as

$\omega=\frac{\Delta \theta}{\Delta t}$

where $\Delta \theta$ is the angular displacement covered in a time interval of $\Delta t$ . Since all the points of the wheel are coeherent (they move together), they all cover the same angular displacement in the same time, so they all have same rotational speed.

16. away from the center of the path.

The tension in the string is responsible for keeping the tin can in circular motion. Therefore, the tension in the string represents the centripetal force, and so it is directed towards the centre of the path. According to Newton's third law, the tin can exerts a force on the string which is equal in magnitude (so, same magnitude of the tension), but opposite in direction: therefore, away from the centre of the path.

17. weight of the bob.

There are two forces acting on the bob in the vertical direction: the weight of the bob (downward) and the vertical component of the string tension (upward). Since there is no acceleration along the vertical direction, the net force must be zero, so these two forces must be equal: it means that the vertical component of the string tension is equal to the weight of the bob. Along the horizontal direction, instead, the horizontal component of the string tension corresponds to the centripetal force that keeps the bob in circular motion.

18. horizontal component of string tension.

Along the horizontal direction, there is only one force acting on the bob: the horizontal component of the string tension. Since the bob is moving of circular motion along the horizontal direction, this means that this force (the horizontal component of the string tension) must correspond to the centripetal force that keeps the pendulum in circular motion.

19. inward, toward the center of swing.

The force that the can exerts on the bug is the force that keeps the bug in circular motion (since it prevents the bug from moving away). Therefore, it must corresponds to the centripetal force.

20. speed of the car. AND radius of curvature.

The normal force exerted on a car executing a turn on a banked track is given by the expression:

$N=\frac{mg}{cos \theta - \mu sin \theta}$

where m is the mass of the car, g is the gravitational acceleration, $\theta$ is the angle of the bank, and $\mu$ is the coefficient of friction.

From the formula, we see that the normal force depends on $\theta$ (the angle of the bank) and $\mu$ (the coefficient of friction), while it does not depend on the speed of the car or on the radius of curvature. Therefore, these two are the correct answers.

3 0

3 years ago

How many Gigameters in 1600 meters

USPshnik [31]

1.6e-6 gl on the rest of your physics its a killer for me too

6 0

3 years ago

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while test flying the new f-22 raptor fighter jet, test pilot bob put the plane in a horizontal loop while flying at the speed o

sveticcg [70]

Given

v = 343 m/s

ac = 5g

ac = 5*9.8 m/s^2

ac = 49 m/s^2

where,

v: velocity

ac = centripetal aceleration

Procedure

We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration ac; centripetal means “toward the center” or “center seeking”.

Formula

$\begin{gathered} a_c=\frac{v^2}{r} \\ r=\frac{v^2}{a_c} \\ r=\frac{(343m/s)^2}{49m/s^2} \\ r=2401\text{ m} \end{gathered}$

The minimum radius not to exceed the centripetal acceleration is 2401 m.

8 0

2 years ago

(m = 4.0 kg) the cockroach rides on the rim (at radius R) of a disk (M = 6.0 kg) that turns about its center like a merry-go-rou

kvasek [131]

Answer:

ω' = 2.5 rad/s

Explanation:

mass of cockroach, m = 4 kg

mass of disk, M = 6 kg

Radius of disc= R

initial angular velocity, ω = 2 rad/s

Let the final angular velocity is ω'

As no external torque is applied, so the angular momentum is constant.

Angular momentum = Moment of inertia x angular velocity

I ω = I' ω'

$\frac{1}{2}\left ( M+m \right )R^{2}\times {2} = \left (\frac{1}{2}MR^{2}+m(0.5R)^{2}) \right )\omega '$

$10R^{2} = 4R^{2}\omega '$

ω' = 2.5 rad/s

5 0

4 years ago

Why is velocity a vector quantity

Jobisdone [24]

Velocity as a Vector Quantity
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4 0

3 years ago

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