3. A particle of mass m is moving in the xy-plane such that its velocity at...

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3. A particle of mass m is moving in the xy-plane such that its velocity at a point (x, y) is given as v = a(yx+2xy), where a is a non-zero constant. What is the force F acting on the particle? (A) F = 2ma (xx+y) F = ma (yx+2xy) (C) F=2ma (yx+x) (D) F=ma (xx+2yy) 4. An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is U, and the speed of sound in the gas is V. At a fixed temperature and pressure, which of the following is the correct option? (A) V3 < V6 and U > U6 (C) vs > V, and U V3 and U3 > U5 (D) vv, and U 5. A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n to n over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab? Monochromatic light wave (n-n)d (A) It will deflect up by an angle tan 2h n 121 (B) It will deflect up by an angle tan-1 (2-)d] (C) It will not deflect (D) The deflection angle depends only on (nz - n) and not on the individual values of n and n = 3. A particle of mass m is moving in the xy-plane such that its velocity at a point (x, y) is given as v = a(yx+2xy), where a is a non-zero constant. What is the force F acting on the particle? (A) F = 2ma (xx+y) F = ma (yx+2xy) (C) F=2ma (yx+x) (D) F=ma (xx+2yy) 4. An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is U, and the speed of sound in the gas is V. At a fixed temperature and pressure, which of the following is the correct option? (A) V3 < V6 and U > U6 (C) vs > V, and U V3 and U3 > U5 (D) vv, and U 5. A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n to n over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab? Monochromatic light wave (n-n)d (A) It will deflect up by an angle tan 2h n 121 (B) It will deflect up by an angle tan-1 (2-)d] (C) It will not deflect (D) The deflection angle depends only on (nz - n) and not on the individual values of n and n =