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Lynna [10]
3 years ago
8

A uniformly charged sphere has a potential on its surface of 450 V. At a radial distance of 7.2 m from this surface, the potenti

al is150 V What is the radius of the sphere?
Physics
1 answer:
Yakvenalex [24]3 years ago
3 0

Answer:

The radius of the sphere is 3.6 m.

Explanation:

Given that,

Potential of first sphere = 450 V

Radial distance = 7.2 m

If the potential of sphere =150 V

We need to calculate the radius

Using formula for potential

For 450 V

V=\dfrac{kQ}{r}

450=\dfrac{kQ}{r}....(I)

For 150 V

150=\dfrac{kQ}{r+7.2}....(II)

Divided equation (I) by equation (II)

\dfrac{450}{150}=\dfrac{\dfrac{kQ}{r}}{\dfrac{kQ}{r+7.2}}

3=\dfrac{(r+7.2)}{r}

3r=r+7.2

r=\dfrac{7.2}{2}

r=3.6\ m

Hence, The radius of the sphere is 3.6 m.

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Instead of moving back and forth, a conical pendulum moves in a circle at constant speed as its string traces out a cone (see fi
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Answer:

a

The  radial acceleration is  a_c  = 0.9574 m/s^2

b

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The vertical Tension is  T_y  =3.3712 j   \ N

Explanation:

The diagram illustrating this is shown on the first uploaded

From the question we are told that

   The length of the string is  L =  10.7 \ cm  =  0.107 \ m

     The mass of the bob is  m = 0.344 \  kg

     The angle made  by the string is  \theta  =  5.58^o

The centripetal force acting on the bob is mathematically represented as

         F  =  \frac{mv^2}{r}

Now From the diagram we see that this force is equivalent to

     F  =  Tsin \theta where T is the tension on the rope  and v is the linear velocity  

     So

          Tsin \theta  =   \frac{mv^2}{r}

Now the downward normal force acting on the bob is  mathematically represented as

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So

       \frac{Tsin \ttheta }{Tcos \theta }  =  \frac{\frac{mv^2}{r} }{mg}

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The centripetal acceleration which the same as the radial acceleration  of the bob is mathematically represented as

      a_c  =  \frac{v^2}{r}

=>  a_c  = gtan \theta

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     a_c  =  9.8  *  tan (5.58)

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substituting value

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    T_y  =  T \ cos \theta  = mg

substituting value

     T_ y  =  0.344 * 9.8

      T_ y  = 3.2712 \ N

The vector representation of the T in term is of the tension on the horizontal and the tension on the vertical is  

         

       T  = T_x i  + T_y  j

substituting value  

      T  = [(0.3294) i  + (3.3712)j ] \  N

         

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