Physics Test 65...

A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and centre of mass velocity V. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are ω_A and ω_B respectively. Then:

The linear momentum, p of a body moving in one dimension varies with time, t according to the equation, p=a+bt², where, a and b are positive constants. The net force acting on the body is:

Mass M is uniformly distributed only on thecurved surface of a thin hemispherical shell. A,B and C are three points inside the shell as shown in the diagram. Let the gravitational potential at points A,B and C be V_A,V_B and V_C, respectively. Then,

Two different gases at the same temperature have equal root mean square velocities (C_rms). If M is the molecular mass of the gas, then:

The refractive index of a material is given by the equation n = A+B / λ², where A and B are constant. The dimensional formula for B is:

A rod of length, l is given two velocities, v₁ and v₂ in opposite directions at its two ends at right angles to the length. The distance of the instantaneous axis of rotation from v₁ is:

The displacement time graph of a moving particle is shown below:

At which point, the instantaneous velocity of the particle is negative?

A hoop of mass M and radius R is hung from a support fixed in a wall. Its moment of inertia about the support is:

The frequency f of vibration of mass m suspended from a spring of spring constant k is given by,

f = cm^xk^y

Where c is dimensionless constant. The values of x and y are respectively: