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Class 10 Class 12

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction µ and the distance x(=QR), are, respectively close to :

• 0.2 and 6.5 m

• 0.2 and 3.5 m

• 0.29 and 3.5 m

• 0.29 and 6.5 m

C.

0.29 and 3.5 m

Energy lost over path PQ = μ mg cos θ x 4

Energy lost over path QR = μ mgx

i.e μ mg cos 30°  x 4 = μ mgx  (∴ θ = 30°)

From Q to R energy loss is half of the total energy loss.

i.e μ mgx = mgh/2
μ = 0.29

The values of the coefficient of friction μ and the distance x (=OR) are 0.29 and 3.5 m

Energy lost over path PQ = μ mg cos θ x 4

Energy lost over path QR = μ mgx

i.e μ mg cos 30°  x 4 = μ mgx  (∴ θ = 30°)

From Q to R energy loss is half of the total energy loss.

i.e μ mgx = mgh/2
μ = 0.29

The values of the coefficient of friction μ and the distance x (=OR) are 0.29 and 3.5 m

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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Give three examples of vector quantities.

Force, impulse and momentum.
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.

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