For the seesaw to be balanced, the system must be in rotational equilibrium. For this to occur, the torque the same on both sides.

The total torque must be equal on both sides in order for the net torque to be zero.

Substitute the formula for torque into this equation.

Now we can use the given values to solve for the missing mass.

The acceleration form gravity cancels from each term.

This problem deals with torque and equilibrium. Noting that the string is between the two masses we can use the torque equation of . We can use the equation to find the torque. Since force is perpendicular to the distance we can use the equation  (sine of 90^o is 1). Force presented in this situation is gravity, therefore F=mg, and using the variable x as a placement for the string we can find r.

x=43, thus the string is placed at the 43cm mark.

In the instant the rope is cut right above the 2kg mass, the pulley now has net torque in the counterclockwise direction because the platform with the masses is still connected to the rope that winds around the pulley. Knowing that , we can determine the torque by knowing that the force (F) on the pulley is due to the tension (T) by the platform. The tension is 19.6N  (equal to the weight) and knowing that the radius of the pulley is 0.25m, we can solve for torque.

Choice 2 is correct.  Think about trying to change a tire…you apply the force on the tire iron as close to perpendicular as possible in order to generate the most force. 

Since the sine of 90 degrees is 1, then you are applying the maximum torque you can generate according to the equation τ = F sin θ.

We are trying to find what force needs to be applied to the rope to result in a net of zero torque on the beam.

Torque applied by the car:

We can use this to find the mass of a student that will create the same amount of torque while hanging from the rope:

The only two factors that affect a pendulum's frequency are the acceleration due to gravity (g) and the length of the pendulum's string (L). This can be seen in the following formula: . 

Both the length of the pendulum's string and the angle of displacement affect the maximum velocity of the pendulum. Increasing the length of the pendulum's string and increasing the angle of displacement both increase the distance the pendulum must travel in a single period, increasing its potential energy at its maximum height, and therefore the maximum velocity at its lowest point.

The key to answering this question is to recall the following important formula for a simple pendulum: .

For a pendulum, the angular velocity is given by the equation , where  is the acceleration due to gravity and  is the length of the pendulum. Of the available answer choices, only changing the length of the string will effect the angular velocity. does not depend on mass or the release point of the pendulum.

The frequency of a pendulum is given by the relation  .

Since gravity on the moon is one sixth of the gravity on Earth, frequency on the moon will be  that on earth.

If the frequency on Earth is , then the frequency of this pendulum on the moon is .