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An object with mass m is spinning in uniform circular motion in a circ

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An object with mass m is spinning in uniform circular motion in a circ  [#permalink]

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15 Dec 2018, 09:16
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Difficulty:

35% (medium)

Question Stats:

69% (02:28) correct 31% (02:30) wrong based on 74 sessions

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An object with mass m is spinning in uniform circular motion in a circle perpendicular to the ground with radius r at a circular velocity of 2 m/s. At the height of its spin, the forces acting on it, f, can be calculated by summing the force due to change in direction and the force due to gravity. The force due to gravity is the mass of the object multiplied by 9.8 m/$$s^2$$. The force due to change in direction is the product of the square of the velocity of the object, the mass of the object, and the reciprocal of the radius. What is m in terms of r and f?

A) $$\frac{f.r}{4 + 9.8r}$$
B) $$\frac{f}{4r + 9.8}$$
C) $$\frac{f.r}{4r + 9.8}$$
D) $$\frac{4r + 9.8}{f}$$
E) $$\frac{(f.r) - 4}{9.8r}$$
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Re: An object with mass m is spinning in uniform circular motion in a circ  [#permalink]

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18 Dec 2018, 07:56
1
OA:A

$$f= 9.8m+\frac{m(2)^2}{r}$$

$$f= \frac{9.8mr+4m}{r}$$

$$f= m*\frac{9.8r+4}{r}$$

$$m=\frac{f*r}{4+9.8r}$$
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Re: An object with mass m is spinning in uniform circular motion in a circ  [#permalink]

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19 Dec 2018, 09:43
1
Option A is the straight forward choice here.

PS: I am slightly astonished whether this is a reading comprehension passage or a Quant question? This question has more to do with careful reading and inference rather than Quant reasoning or Algebraic manipulations!! Just Saying!!
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An object with mass m is spinning in uniform circular motion in a circ  [#permalink]

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19 Dec 2018, 16:28
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cristianosubo wrote:
An object with mass m is spinning in uniform circular motion in a circle perpendicular to the ground with radius r at a circular velocity of 2 m/s. At the height of its spin, the forces acting on it, f, can be calculated by summing the force due to change in direction and the force due to gravity. The force due to gravity is the mass of the object multiplied by 9.8 m/$$s^2$$. The force due to change in direction is the product of the square of the velocity of the object, the mass of the object, and the reciprocal of the radius. What is m in terms of r and f?

A) $$\frac{f.r}{4 + 9.8r}$$
B) $$\frac{f}{4r + 9.8}$$
C) $$\frac{f.r}{4r + 9.8}$$
D) $$\frac{4r + 9.8}{f}$$
E) $$\frac{(f.r) - 4}{9.8r}$$

Given;

Mass of object $$= m$$

Velocity of the object $$= 2$$

Radius $$= r$$

Force $$"f"$$ $$=$$ Force due to change in direction $$+$$ Force due to gravity

Force due to change in direction $$=$$ $$($$Square of velocity of the object $$*$$ mass of the object $$)/$$Radius $$=> \frac{2^2*m}{r} = \frac{4m}{r}$$

Force due to gravity $$=$$ mass of object $$* 9.8 => m*9.8$$

Therefore; $$f = \frac{4m}{r} + m*9.8 = m(\frac{4}{r}+9.8)$$

$$f = m (\frac{4 + 9.8*r}{r})$$

$$m = \frac{f*r}{4+9.8r}$$

An object with mass m is spinning in uniform circular motion in a circ   [#permalink] 19 Dec 2018, 16:28
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