Ahot-air balloon consists of a basket hanging beneath a large envelope filled with hot air. a typical hot-air balloon has a total mass of 534 kg, including passengers in its basket, and holds 2.77 ✕ 103 m3 of hot air in its envelope. if the ambient air density is 1.23 kg/m3, determine the density (in kg/m3) of hot air inside the envelope when the balloon is neutrally buoyant. neglect the volume of air displaced by the basket and passengers. hint kg/m3

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

Aperson stands on a platform, initially at rest, that can rotate freely without friction. the moment of inertia of the person plus the platform is ip. the person holds a spinning bicycle wheel with its axis horizontal. the wheel has moment of inertia iw and angular velocity ωw. take the ωw direction counterclockwise when viewed from above. part a what will be the angular velocity ωp of the platform if the person moves the axis of the wheel so that it points vertically upward?

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?