Balloon in a Car

You are sitting in a motionless car, which is tightly sealed, i.e. no open windows, holes in the car, etc. A helium balloon on a string is tied to the floor. If you start accelerating the car, is the balloon going to move back, forward, or stay in place?

The reason the balloon floats up in the air is that the helium has a lower density, so when gravity pulls the denser air around down, the balloon gets pushed up. Similarly, when the car accelerates, the air around gets drawn to the back of the car, which makes the helium balloon go forward.

Front Wheels

When a car is making a turn, are its front wheels parallel to each other?

The front wheels are not parallel to each other. The reason is that when steering, all wheels are turning along circles which have a common center. Otherwise, the car would be drifting.

The Golden Cylinder

You are shown two cylinders – one of them is made of gold and hollow, the other one is made of alloy and solid. Both of them have the same weight, shape, and are colored in black. How can you figure out which cylinder is the golden one, without scratching the paint?

Simply roll the two cylinders on the ground. The hollow one will roll farther than the solid one since it will have a higher moment of inertia.

Meg’s Height

Four years ago, Meg put a nail on a tree in order to mark her height. If the tree grows 10 inches per year, and currently the nail is 5 inches lower than Meg, how much has Meg grown over these four years?

Five inches. Trees grow at their tops.