a-level physics question

A simple pendulum has a time period of 1.42 s on Earth. The gravitational field strength at the surface of Mars is 0.37 times that at the surface of the Earth. What is the time period of the pendulum on Mars?

I know the answer is 2.3 seconds but can someone show me the solution?

Do you know the length of the pendulum? If not, you are given enough information to work it out, right?

$T_{Mars} = 2\pi{\sqrt \frac{L}{0.37g}}$

No that was not given , I worked it out to be about 0.5. But i've just realised I thought 0.37 times meant 0.37 times more , so I got the wrong number for g. I think I have it right now, though I am like 0.01 out, it will do.

But thanks for helping!

I have another questions though:

1)
A Rotor has a diameter of 4.5 m. It accelerates uniformly from rest to maximum angular velocity in 20 s.The total moment of inertia of the Rotor and the riders is 2.1 × 10⁵ kg m².(b) (i) At the maximum speed the centripetal acceleration is 29 m s^–2.Show that the maximum angular velocity of a rider is 3.6 rad s^–1.



2)
Calculate the centripetal force acting on a rider of mass 75 kg when the ride is moving at its maximum angular velocity.Give your answer to an appropriate number of significant figures.

The answer to this is 2200 newtons and I got 432, so I think i was missing something , i used the normal centripetal force formula: f=mv^2/r

(these are part of the same question btw)

As for part 1, you're given the diameter, the time and the maximum centripetal acceleration. You need to find maximum angular velocity. Find an equation and that suits these three variables and you'll get your answer.

As for part 2, I would not use F = (mv^2)/r simply because you don't know the instantaneous velocity. Use the other equation F = mrω^2. You'll need your angular velocity from part a (as you said both parts are from the same question) and that should be it.

Easiest way to tackle these questions is to write down the variables you know and see if there is any equation that is suitable to solve your unknown.