g Consider two blocks of masses m1 and m2 at the top of two frictionless inclines, respectively. Both blocks start to slide down from rest at the same height. However, the incline on which m1 sits is at an angle of 20° with the horizontal, while the incline on which m2 sits is at 45°. Which block will be going faster at the bottom of its incline?

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27 April, 14:51

g Consider two blocks of masses m1 and m2 at the top of two frictionless inclines, respectively. Both blocks start to slide down from rest at the same height. However, the incline on which m1 sits is at an angle of 20° with the horizontal, while the incline on which m2 sits is at 45°. Which block will be going faster at the bottom of its incline?

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Gregory · Answer 1

acceleration of an object on an inclined plane due to gravitational pull

= g sinθ. This acceleration is irrespective of mass of the object coming down. It only depends on the inclination.

If θ is larger, sinθ will be larger hence gravitational acceleration on inclined surface will be greater. It happens so because a component of weight mg is acting on the body. This component is mgsinθ. The other component mgcosθ acts perpendicular to surface hence it does not contribute to its acceleration.

acceleration produced = force / mass

= mgsinθ / m

= gsinθ.

in the given case, the inclination of plane with mass m₁ is less, hence its downward acceleration will be lesser as compared with the acceleration of m₂ which is put on a surface with greater inclination.