A game of "Country Erasers" is played with two identical square-shaped erasers of length ℓ , thickness h and uniform mass m . They initially lie flat beside each other on a horizontal table, with thei

Question

A game of "Country Erasers" is played with two identical square-shaped erasers of length $ℓ$ , thickness h and uniform mass m . They initially lie flat beside each other on a horizontal table, with their ends a distance $d > h$ apart. In a winning move, a player flicks one eraser towards the other, such that it rotates vertically and eventually lands resting flat on the other eraser, as shown below. Assume that neither of the erasers slip at any point of contact with the table or with each other throughout their motion.

TestHub · Accepted Answer

The flicked eraser topples about its bottom corner. To stand on end its CM must rise from $\frac{h}{2}$ to $\frac{ℓ}{2}$ : minimum flick energy $E = \frac{m g ( ℓ - h )}{2}$ - (B) correct.

Geometry of the rotation about the contact corner gives the maximum separation $d_{ma x} = h + \frac{ℓ ^{2}}{4} - h^{2}$ - (A) correct.

Finally it rests flat on the other eraser, having gained $Δ PE = m g h$ ; dissipated energy = $E - Δ PE = \frac{m g ( ℓ - 3 h )}{2}$ - (C) correct. The move is possible - (D) incorrect.

Correct options: A, B, C

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Options:(select one or more)

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