A 10 kg block is at rest as shown on a horizontal surface having a coefficient of static friction of 0.7. String-1 is horizontal and string-2 makes an angle of $3 0^{\circ}$ with the vertical. A mass M hangs from string-3. Which of the following statement(s) about this situation is/are true? ( $g = 10 m / s^{2}$ )

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Let T1, T2, T3 be the tensions in strings 1, 2 and 3. At the knot, string-3 carries the hanging mass: T3 = Mg.

Knot balance along the vertical (string-2 makes $3 0^{\circ}$ with the vertical):

$T_{2} cos 3 0^{\circ} = T_{3} = M g$

Knot balance along the horizontal:

$T_{1} = T_{2} sin 3 0^{\circ}$

$\frac{T _{1}}{T _{3}} = tan 3 0^{\circ}$

So statement (B) is true.

The tension T1 is balanced by the static friction on the 10 kg block; its maximum value is:

$T_{1 (m a x)} = f_{m a x} = μ N = 0.7 \times 10 \times 10 = 70 N$

So statement (A) is true.

For the largest hanging mass, T1 = 70 N with $T_{1} = M g tan 3 0^{\circ}$ :

$M_{m a x} = \frac{70}{g tan 3 0 ^{\circ}} = \frac{70}{10} 3 = 73 \approx 12 k g$

So statement (C) is true and (D) is false.

Hence the correct options are (A), (B) and (C).

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Options:(select one or more)

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