The potential energy of particle varies with distance x fixed a origin as $v = \left(\frac{A\sqrt{x}}{x + B}\right)$; where A and B are constants. The dimensions of AB are

• [ M L^5/2 T^-2 ]

• [ M L² T^-2 ]

• [ M^3/2 L^3/2 T^-2 ]

• [M L^7/2 T^-2 ]

A solid sphere and a hollow sphere of the same material and of a same size can be distinguished without weighing

• by determining their moments of inertia about their coaxial axe

• by rolling them simultaneously on an inclined plane

• by rotating them about a common axis of rotation

• by applying equal torque on them

A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component is (approximately)

• 20 m

• 7.2 m

• 5.0 m

• 4.5 m

A coin is dropped in a lift. It takes time t₁  to reach the floor when lift is stationary. It takes time t₂ when lift is moving up with constant acceleration. Then,

• t₁ ≥ t₂

• t₂ > t₁

• t₁ = t₂

• t₁ >> t₂

A body is thrown with a velocity of 9.8 m/s making an angle of 30° with the horizontal. It will hit the ground after a time

• 1.5 s

• 1 s

• 3 s

• 2 s

Three points charges +q, -2q and +q are placed at points (x=0,  y=a,  z=0),  ( x=0,  y=0,  z=0 )  and  (x=a,  y=0,  z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

• √2 qa along + y direction

• √2 qa along the line joining point

• qa along the line joining points (x = 0,y = 0, z = 0) and (x = a, y = a, z = 0)

• √2 qa along + x direction

The angle between two linear transmembrane domains is defined by following vectors $\mathrm{a} = \hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}} \mathrm{and} \mathrm{b} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$

• cos^-1 $\left(\frac{1}{3}\right)$

• cos^-1 $\left(\frac{-1}{3}\right)$

• sin^-1 $\left(\frac{-1}{3}\right)$

• sin^-1 $\left(\frac{1}{3}\right)$

A projectile is fired with a velocity u at angle θ with the ground surface. During the motion at any time it is making an angle a with the ground surface. The speed of particle at this time will be

• ucosθ sec$\mathrm{\alpha }$

• ucosθ tan$\mathrm{\alpha }$

• u² cos²$\mathrm{\alpha }$ sin²$\mathrm{\alpha }$

• usinθ.sin$\mathrm{\alpha }$

Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

• $\mathrm{h} = \frac{\mathrm{H}}{2}$

• $\mathrm{h} = \frac{3\mathrm{H}}{2}$

• $\mathrm{h} = \frac{2 \mathrm{H}}{3}$

• h = $\frac{3}{4}\mathrm{H}$

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?