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Class 10 Class 12

A roller coaster is designed such that riders experience " weightlessness" as they go round the top of a hill whose radius of curvature is 20 m.  The speed of the car at the top of the hill is between

• 14 m/s and 15 m/s

• 15m/s and 16 m/s

• 16 m/s and 17 m/s

• 13m/s and 17 m/s

A.

14 m/s and 15 m/s

Balancing the forces, we get
Mg-N = Mv2/R
For weightlessness, N = 0
therefore, MV2/R = Mg
where R is the radius of curvature and v is the speeds of the car.
Therefore,

Thus, the speed of the car at the top of the hill is between 14 m/s and 15 m/s

Balancing the forces, we get
Mg-N = Mv2/R
For weightlessness, N = 0
therefore, MV2/R = Mg
where R is the radius of curvature and v is the speeds of the car.
Therefore,

Thus, the speed of the car at the top of the hill is between 14 m/s and 15 m/s
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What is Geocentric theory?

According to the geocentric theory, all the astronomical bodies like the moon, the sun and stars revolve around the earth, and the earth is at the centre of the universe.
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The position co-ordinates of two particles of masses m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m1 and m2 are respectively,

Let the position coordinates of the centre of mass be (X, Y, Z).

Therefore the position vector of centre of mass is,

Since,

Comparing the coefficients of  , we get

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