Given that y = a cos, where t represents time in second and x represents distance in metre. Which of the following statements is true ?
A ball is thrown vertically upward with a speed v from a height h meters above the ground. The time taken for the ball to hit ground is
Now retain only the positive sign.
A long spring is stretched by 2 cm. Its potential energy is U. If the spring is streched by 10 cm, its potential energy would be
We know, potential energy of spring is given by (1/2)kx^2 where k is spring constant and x is stretched distance.
Here , x=2cm so, U=(1/2)k*2^2=2k
For, x=10cm :-
Final potential energy will be 25U.
A sphere A of mass m moving with constant velocity u hits another stationary sphere B of the same mass in a head on collision. if e is the coefficient of restitution, what is the ratio of velocities of sphere A to the sphere B after collision?
The radius of gyration of a uniform rod of length L about on axis passing through its centre of mass is
In case of an orbiting satellite if the radius of orbit is decreased
KE=I w²=Iv²/r² ( since omega =v/r)
This implies that KE is inversely proportional to r²
So when radius is decreased , KE will increase due to which PE will decrease
Hence option D is correct.
Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative
A system undergoes a cyclic process in which it absorbs Q1 heat and gives out Q2 heat. The efficiency of the process is η and work done is W. Select the correct statement
Concept: Carnot engine. Explanation: Heat is transferred to the working material (Q1) and heat is rejected during (Q2). The thermal efficiency is ηth = W/Q1. Applying first law, we have, W = Q1 − Q2. ηth = 1 − Q2/Q1. Hence, correct answer is (b).
A cylinder of radius R, made of a material of thermal conductivity k1, is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The shell is made of a material of thermal conductivity k2. The two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
In the arrangement shown coefficient of friction between the two blocks A and B is 0.6 and ground is frictionless. Force constant of spring is 900 N/m. Find the maximum elongation of spring (in cm) such that the blocks do not slip over each other when released.
Two particles A & B are projected from top of two towers of height 300 m and 600 m with velocity 50 m/s and 250 m/s respectively. The angular velocity of B wrt A is α rad/min. Fill the value of 10a in OMR sheet
A sphere of radius r is projected up an inclined plane for which with a velocity v0 and initial angular velocity . The total time of rise is found to be Find k.
A hemispherical bowl of radius R = 0.1m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10–2 kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure 'g' using this set up, by measuring h accurately. Assuming that R and ω are known precisely and that the least-count in the measurement of h is 10–4 m, the numerical value of minimum possible error Δg in the measured value of g is given by α x 10–2 m/s2. Fill the value of α in OMR sheet.
A bimetallic strip consisting of a brass strip and a steel strip, each of length 1 m and each of thickness 0.5 cm is clamped at one end as shown in figure. Calculate the depression to the nearest integer (in cm) of the free end when it is heated by 100ºC.
[Take : αiron = 11 × 10–6 K–1; αbrass = 19 × 10–6 K–1]