Question

A cubical block of mass 6 kg and side 16.1 cm is placed on a frictionless horizontal surface. It is hit by a cue at the top to impart impulse in the horizontal direction. The minimum impulse imparted to topple the block must be greater than ______ kg m/s.

विकल्प

• 1.00

• 2.00

• 3.00

• 4.00

Answer 1

A cubical block of mass 6 kg and side 16.1 cm is placed on a frictionless horizontal surface. It is hit by a cue at the top to impart impulse in the horizontal direction. The minimum impulse imparted to topple the block must be greater than 4.00 kg m/s.

Explanation:

Let

a = side of the cube

p = impulse imparted

∴ After hitting,

v₀ = `p/m`

and `omega_0 = (pa)/(2I)`

I : the moment of inertia about the axis passing through C.M.

For just toppling,

`1/2Iomega_0^2 = mg  a(1/sqrt2 - 1/2)`

(Applying energy conservation between situations A and B.)

⇒ p = `(2Iomega_0)/a`

= 4 kg m/s