A particle describes a horizontal circle on the smooth surface of an inverted cone. The plane of that circle is at a height of 9.8cm above the vertex. Then the speed (in ms^-1) of the particle is ................× 10^–2

Particle on Inverted Cone

Particle on Inverted Cone: Speed Calculation

Given the scenario, a particle moves in a horizontal circle on the smooth surface of an inverted cone, with the circle's plane at a height of 9.8 cm above the vertex.

To find the speed, the relationship between the height h, gravitational acceleration g, and the cone's semi-vertical angle θ is used. The speed is derived as:

v = √(g · h · tan²θ)

If we use tanθ = 1 (i.e., a cone angle of 45 degrees), this simplifies to:

v = √(g · h)

Substituting the values:

• h = 9.8 cm = 0.098 m
• g = 9.8 m/s²

v = √(9.8 × 0.098) = √(0.9604) = 0.98 m/s

When expressed as x × 10⁻² m/s, this is:

0.98 × 100 = 98 × 10⁻² m/s

So, the speed of the particle is 98 × 10⁻² m/s.