A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are $\left(\sqrt{3}, 3\right)$. The path of the particle makes with the x-axis an angle of

• 30^o

• 45^o

• 60^o

• 0^o

A wheel has angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2 s it has rotated through an angle (in radian) of

• 6

• 10

• 12

• 4

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius  R with constant speed v. The time period of the motion

• depends on v and not on R

• depends on both R and v

• is independent of both R and v

• depends on R and not on v

A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d The average speed for this round trip is

• $\frac{2 {\mathrm{\nu }}_{\mathrm{d} }{\mathrm{\nu }}_{\mathrm{u}}}{{\mathrm{\nu }}_{\mathrm{d}} + {\mathrm{\nu }}_{\mathrm{u}}}$

• $\sqrt{{\mathrm{v}}_{\mathrm{u} }{\mathrm{v}}_{\mathrm{d}}}$

• $\frac{{\mathrm{v}}_{\mathrm{d} }{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}} + {\mathrm{v}}_{\mathrm{u}}}$

• $\frac{{\mathrm{v}}_{\mathrm{u}} + {\mathrm{v}}_{\mathrm{d}}}{2}$

A block B is pushed momentarily along a horizontal surface with an initial velocity v. If µ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time

• $\frac{\mathrm{\nu }}{\mathrm{g\mu }}$

• $\frac{\mathrm{g\mu }}{\mathrm{\nu }}$

• $\frac{\mathrm{g}}{\mathrm{\nu }}$

• $\frac{\mathrm{\nu }}{\mathrm{g}}$

Two satellites of earth, S₁ and S₂ are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statements is true ?

• The time period of S₁ is four times that of S₂

• The potential energies of earth and satellite in the two cases are equal

• S₁ and S₂ are moving with the same speed

• The kinetic energies of the two satellites are equal

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is

• -0.5 J

• -1.25 J

• 1.25 J

• 0.5 J

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45° with the initial vertical direction is

• $\mathrm{Mg} \left(\sqrt{2} + 1\right)$

• $\mathrm{Mg} \sqrt{2}$

• $\frac{\mathrm{Mg}}{\sqrt{2}}$

• $\mathrm{Mg} \left(\sqrt{2} -1\right)$

A force of $-\mathrm{F} \hat{\mathrm{k}}$ acts on O, the origin of the coordinate systems. The torque about the point (1, -1 ) is

• $\mathrm{F} \left(\hat{\mathrm{i}} - \hat{\mathrm{j}}\right)$

• $- \mathrm{F} \left(\hat{\mathrm{i}} + \hat{\mathrm{j}}\right)$

• $\mathrm{F} \left(\hat{\mathrm{i}} + \hat{\mathrm{j}} \right)$

• $-\mathrm{F} \left(\hat{\mathrm{i}} - \hat{\mathrm{j}}\right)$

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

• [ M L² T^-3 I^-1]

• [M L² T^-1]

• [M L² T^-1 I^-1]

• [M L² T^-3 I^-2 ]