If the position of a moving particle, with respect to time be, x(t) = 1 + t − t², then, the acceleration of particle is given by (assume all measurements in MKS)

• − 1 ms^-2

• − 1.5 ms^-2

• − 2 ms^-2

• − 2.5 ms^-2

A ball is dropped from a tower of height h. The duration (t₀) of motion, when it reaches bottom of the tower is given by

• $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}$

• $\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

• $2 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

• $4\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$

For the given position-time (x − t) graph , the interval in  which velocity is zero, is

• (t₃ − t₁)

• (t₃ − t₂)

• (t₅ − t₄)

• (t₅ − t₂)

4.

A particle moves along the x-axis as x = u (t −2s) + a (t − 2s)². The initial velocity of the particle is

• u − 2a

• u − 4a

• 2a − u

• 2a − 3u

The centre of mass of three particles of mass m₁ = 1.0 kg, m₂ = 2.0 kg, and m₃ = 3.0 kg at the corners of an equilateral triangle 1.0 m on a side, as shown in figure

• $\left(\frac{7}{12}\mathrm{m}, \frac{\sqrt{3}}{4}\mathrm{m}\right)$

• $\left(\frac{5}{12}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

• $\left(\frac{5}{13}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

• $\left(\frac{8}{12}\mathrm{m}, \frac{\sqrt{3}}{5}\mathrm{m}\right)$

A system consists of two point masses M and m (< M). The centre of mass of the system is

• at the middle of m and M

• nearer to M

• nearer to m

• at the position of large mass

A ball is projected horizontally with a velocity of 5 m/s from the top of a building 19.6 m high, flow long will the ball take to hit the ground?

• $\sqrt{2} \mathrm{s}$

• 2 s

• $\sqrt{3} \mathrm{s}$

• 3 s

A body of mass 3 kg is acted on by a force which varies as shown in the graph. The momentum acquired is given by

• zero

• 5 N-s

• 30 N-s

• 50 N-s

Two perfectly elastic particles A and B of equal masses travelling along the line joining, them with velocity 15 m/s and 20 m/s respectively collide. Their velocities after the elastic collision will be (in m/s) respectively.

• 0 and 25

• 5 and 20

• 10 and 15

• 20 and 15

A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The  velocity of the 12 kg mass is 4 ms^-1 . The kinetic energy of the other mass is

• 192 J

• 96 J

• 144 J

• 288 J