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Figure below shows a shampoo bottle in a perfect cylindrical shape In a simple experiment, the stability of the bottle filled with different amount of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle theta depicts the critical angular displacement resulting in the bottle losing its stability and tripping over. Choose the graph correctly depicting the fraction f of shampoo filled (f= 1 corresponds to completely filled) vs the tripping angle theta

Following reactions are known as inverse beta decay p+vecvrarrn+e^(+) n+vrarrp+e^(-) These reactions have extremely low probabilities. Because of this, neutrinos and antineutrinos are able to pass through vast amount of matter without any interaction. In an experiment to detect neutrinos, large number of neutrinos coming out from beta decays of a radioactive material were made to pass through a tank of water, containing a cadmium compound in solution, which provided the protons to interact with antineutrinos, which provided the protons to interact with antineutrinos. Immediately after a proton absorbed a neutrino to yield a positron and a neutron, the positron encountered an electron and both got annihilated. the gamma ray detectors surrounding the tanks responded to the resulting photons. This confirmed that the above reaction has taken place. (a) How many gamma ray photons are produced when a electron annihilates with a positron? What is energy of each photon? Take the mass of an electron to be 0.00055 u. (b) The neutron produced in the above reaction was captured by .^(112)Cd to form .^(113)Cd . The atomic masses of these two isotopes of cadmium are are 111.9028u and 112.9044u respectively. mass of a neutron is 1.0087u. find the Q value of this reaction. Assume half of this energy is excitation energ of .^(113)Cd . if the nucleus de-excites by emitting a gamma ray photon find its wavelenght.

Arrange the following steps of an experiment in a sequential order to determine the frequency of a simple pendulum. (A) Start the stop watch when the bob reaches the extreme position and count the number of oscillations.(B) Suspend a simple pendulum from a cork fixed to a stand. (C) Repeat the experiment and determine the time taken for 20 oscillations. (t_(2)) (D) Pull the bob of the simple pendulum from its initial position of rest and release. (E) Stop the stop watch at the end of 20 oscillations and determine the time taken to complete 20 oscillations (t_(1)) . (F) Determine the average of t_(1) and t_(2) as t. (G) The time period of the oscillation is found using. T = (t)/(20) and frequency using, f = 1/T .