PhysicsGutka

Q1 . A cyclist and his bicycle has a mass of 80 kg. After 100m he reaches the top of a hill, with slope 1 in 20 measured along the slope, at a speed of 2 m/s. He then free wheels the 100m to the bottom of the hill where his speed has increased to 9m/s. How much energy has he lost on the hill? Solution Figure 3.3: Dimensions of the hill in worked example 3.5 If the hill is 100m long then the height is: So potential energy lost is Increase in kinetic energy is By the principle of conservation of energy

Q1 . The speed of a projectile when it is at its greatest height is √2/5 times its speed at half the maximum height. Find out the angle of projection. Solution  :- Let  θ be the angle of projection and u its initial speed. Then maximum height will be, H = u 2 sin 2 θ/2g So, gH = u 2 sin 2 θ /2 Now, v H  = u cosθ Or, v H 2  = u 2  cos 2 θ                  …... (1) v H/2 2  = u 2 -2g(H/2) = u 2 -gH v H/2 2 = u 2 -(u 2 sin 2 θ/2)             …...(2) Now it is given that, v H  = [ √2/5] v H/2 Or, v H 2  = (2/5)  v H/2 2 Substituting the values from equations (1) and (2), we get, (u 2  cos 2 θ) = 2/5 [u 2 -(u 2 sin 2 θ/2)] Or, 5cos 2 θ = 2[1-(sin 2 θ/2)] Or, 5(1-sin 2 θ) = 2-sin 2 θ Or, sin 2 θ = ¾ Or, sinθ = ( √3)/2, Or,  θ = 60 o Thus from the above observation, we conclude that, the angle of projection would be  60 o . Q2 :- A gun moving at a speed of 30m/sec fires at an angle 30 o  with a velocity 150m/s relative to the gun. Find the distance be

In 1801 Thomas Young was able to offer some very strong evidence to support the wave model of light. He placed a screen that had two slits cut into it in front of a monochromatic ( single color ) light. The results of Young's Double Slit Experiment should be very different if light is a wave or a particle. Let’s look at what the results would be in both situations, and then see how this experiment supports the wave model. If light is a particle… We set up our screen and shine a bunch of monochromatic light onto it. If light is a particle, then only the couple of rays of light that hit exactly where the slits are will be able to pass through. Imagine it as being almost as though we are spraying paint from a spray can through the openings. Since they are little particles they will make a pattern of two exact lines on the viewing screen ( Figure 1 ). Figure 1 If light is a wave… If light is a wave, everything starts the same way, but results we get are v