Question

A cubical block of mass m slides in an inclined right angled trough as shown in the figure. If the coefficients of kinetic friction between block and material composing the trough is μk, find the acceleration of the block. (Both walls of the trough make an angle of 45^{∘} with the inclined plane)

- g(sinθ−√2μkcosθ)
- g(sinθ−μkcosθ)
- g(sinθ−2μkcosθ)
- g(sinθ−√μkcosθ)

Solution

The correct option is **A** g(sinθ−√2μkcosθ)

Equation of motion of the block is

ma=mgsinθ−2μkmgcosθcos45∘.

(Net force = Gravitational force + Frictional force)

In the second term on the right side of above equation factor 2 arises due to the fact that frictional force arises from two walls of the trough, and term cos45∘ takes care of the fact that the walls are tilted at 45∘ to the axis of channel, and the normal reaction is accordingly reduced.

∴a=g(sinθ−√2μkcosθ)

Hence, the correct answer is option (a).

Equation of motion of the block is

ma=mgsinθ−2μkmgcosθcos45∘.

(Net force = Gravitational force + Frictional force)

In the second term on the right side of above equation factor 2 arises due to the fact that frictional force arises from two walls of the trough, and term cos45∘ takes care of the fact that the walls are tilted at 45∘ to the axis of channel, and the normal reaction is accordingly reduced.

∴a=g(sinθ−√2μkcosθ)

Hence, the correct answer is option (a).

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