A pulley systemis attached to a massless board as shown below. The board pivots only at the pivot point. A `10 g` mass `M` sits exaxtly in the middle of the board. If the angle `theta` is `60^@`, what is the force `F(i n N)` necessary to hold the board in the position shown.
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A mass m is attached to a rigid rod of negligible mass as shown in figure. The system is pivoted at point O and rotates about the indicated z -axis with angular velocity vec(omega) , maintaining a fixed angle theta with the axis.

A uniform bar of mass m is supported by a pivot at its top about which the bar can swing like a pendulum. If a force F is applied perpendicular to the lower end of the bar as shown in figure, what is the value of F in order to hold the bar in equilibrium at an angle (theta) from the vertical

A uniform bar of mass m is supported by a pivot at its top about which the bar can swing like a pendulum. If a force F is applied perpendicular to the lower end of the bar as shown in figure, what is the value of F in order to hold the bar in equilibrium at an angle (theta) from the vertical

Two painters are working from a wooden hoard 5 m long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of 1040 N . Painter A of mass 80 kg is working at a distance of 1 m from one end. Painter B of mass 60 kg is working at a distance of x in from the centre of mass of the board on the other side. Take mass of the board as 20 kg and g = 10ms^(-2) . The range of x so that both the painters can work safely is

Board A is placed on board B as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed 6 m/ s. Board B hits a resulting board C "head·on". After the collision, board B and C stick together and board A slides on top of board C and stops its motion relative to C in the position shown on the diagram. What is the length (in m) of each board? All three boards have the same mass, size and shape. The coefficient of kinetic friction between boards A and C and between board A & B is 0.3