1. A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice.
[Take atmospheric pressure = 1.0 × 10^5 N/m², density of water = 1000 kg/m³ and g = 10 m/s². Neglect any effect of surface tension.]
2. A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.
3. A metal rod AB of length 10x has its one end A in ice at 0°C and the other end B in water at 100°C. If a
point P on the rod is maintained at 400°C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of λx from the ice end A, find the value of λ.
[Neglect any heat loss to the surrounding.]
Source: 2009 JEE paper 2
4. The moment of inertia of a uniform disc about its diameter is I. Then the moment of inertia about an axis passng through its centre and perpendicular to its plane is 2I. State true or false.
5. A particle executes a linear simple harmonic motion of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points located at 12.5 cm on either side of equilibrium position?
a. 2.5 s b. 1.5 sec c. 0.5 sec d. 3.0 sec
4 and 5 (non JEE)