A force F is given F = at + bt² where, t is time. What are the dimensions of a and b?

• [ M L T^-1 ] and [M L T^o ]

• [ M L T^-3 ] and [ M L² T^-4 ]

• [ M L T^-4 ] and [ M L T¹ ]

• [ M L T^-3 ] and [ M L T^-4 ]

A particle moves towards east for 2 s with velocity 15 m/s and move towards north for 8 s with velocity 5 m/s. Then, average velocity of the particle is

• 1 m/s

• 5 m/s

• 7 m/s

• 10 m/s

The distance x (in µm) covered by a molecule starting from point A at time t = 0 and stopping at another point B in given by the equation  $\mathrm{x} = {\mathrm{t}}^2 \left(2 - \frac{\mathrm{t}}{3}\right)$ The distance between A and B ( in μm) is closed to

• 10.7

• 20.7

• 40.7

• 50.7

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is     

• $\frac{3 \mathrm{cl} + 2 \mathrm{D} {\mathrm{l}}^2}{3 \left( 2\mathrm{c} + \mathrm{D} \mathrm{l} \right)}$

• $\frac{2 \mathrm{cl} + 3\mathrm{D} {\mathrm{I}}^2}{2 \left( 4\mathrm{c} + 8\mathrm{I} \right)}$

• $\frac{2 \mathrm{cl} + 3 {\mathrm{DI}}^2}{3 \left(2\mathrm{c} + \mathrm{I}\right)}$

• $\frac{\mathrm{cl} + {\mathrm{DI}}^2}{2 \left( 2 \mathrm{c} + \mathrm{DI} \right)}$

A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s². Find the displacement of the block during the first 0.2 s after the start. (Take, g = 10 m/s²)

• 30 cm

• zero

• 20 cm

• 25 cm

A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be

• $\sqrt{3} {\mathrm{ms}}^{-1}$

• $\frac{2}{\sqrt{3}} {\mathrm{ms}}^{-1}$

• $\sqrt{2} {\mathrm{ms}}^{-1}$

• $\frac{\sqrt{5}}{2} {\mathrm{ms}}^{-1}$

The displacement x of a particle varies with time t as x = ae^-αt + be^βt where a, b, $\mathrm{\alpha }$ and β are positive constants. The velocity of the particle will

• decrease with time

• be independent of $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$

• drop to zero when $\mathrm{\alpha } = \mathrm{\beta }$

• increase with time

If A + B = C and that C is perpendicular to A. What is the angle between A and B, if $\left|\mathrm{A}\right| = \left|\mathrm{B}\right|$

• $\frac{\mathrm{\pi }}{4}$ rad

• $\frac{\mathrm{\pi }}{2}$ rad

• $\frac{3 \mathrm{\pi }}{4}$ rad

• $\mathrm{\pi }$ rad

139.

A body is whirled in a horizontal circle of radius 25 cm. It has an angular velocity of 13 rad/s. What is its linear velocity at any point on circular path?

• 2 m/s

• 3 m/s

• 3.25 m/s

• 4.25 m/s

Assertion: If  α =  - 2t for a particle moving in a straight line starting with initial velocity 4 m/s from the origin, then distance travelled by it in 2 s is same as displacement.

Reason: Velocity changes direction after 2 s only.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.