Physics

The force is given in terms of time t and displacement x by the equation
F = A cos Bx + C sin Dt
The dimensional formula of AD/B is :

In the given figure, there is a circuit of potentiometer of length AB = 10m. The resistance per unit length is 0.1Ω per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :
(The diagram shows a primary circuit with a 6V battery and a 20Ω resistor connected across the potentiometer wire AB. The secondary circuit shows an emf source being measured.)

The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt², where α and β are constants. The distance travelled by the particle between 1s and 2s is :

A heat engine has an efficiency of 1/6. When the temperature of sink is reduced by 62°C, its efficiency get doubled. The temperature of the source is :

A linearly polarized electromagnetic wave in vacuum is E = 3.1 cos[(1.8)z - (5.4 * 10?)t] î N/C. Is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has radius equal to :

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :
(The graph shows Temperature (°C) on the y-axis and Time (s) on the x-axis. Both A and B are straight lines starting from the origin. For body A, temperature reaches 120°C in 4s. For body B, temperature reaches 90°C in 6s.)

If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb can be expressed as:

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

A force F = (40î + 10?)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10s, will be :