Motion in A Plane

Two bodies are thrown up at angles of 40° and 60°, respectively, with the horizontal. If both bodies attain the same vertical height, then the ratio of velocities with which these are thrown is:

• $\sqrt{\frac{2}{3}}$

• $\frac{2}{\sqrt{3}}$

• $\sqrt{\frac{3}{2}}$

• $\frac{\sqrt{3}}{2}$

An arrow is shot, its range is 200 m and its time of flight is 5 s. If g =10 m/s², then the horizontal component of velocity of the arrow is :

• 12.5 m/s

• 250 m/s

• 31.25 m/s

• 40 m/s

If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if :

• a_r = 0 and a_t = 0

• a_r = 0 and a_t ≠ 0

• a_r ≠ 0 and a_t = 0

• a_r ≠ 0 and a_t ≠ 0

Mark the correct option.
If a ball is projected with velocity v₀ at an angle of elevation 30°, then

• gravitational potential energy will, be minimum at the highest point of the trajectory

• kinetic energy will be zero at the highest point of the trajectory

• vertical component of momentum will be conserved

• horizontal component of momentum will be conserved

A wheel completes 2000 turns in completing a distance of 9.5 km, then diameter of the wheel is

• 1.5 m

• 1.5 cm

• 7.5 m

• 7.5 cm

A glass marble projected horizontally from the top of a table falls of a distance x from the edge ofthe table. If h is the height of the table, then the velocity of projection is

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

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

• gxh

• g x + h

If a and b are two vectors, then the value of

      (a × b) × (a − b) is

• 2 (b x a)

• − 2(b x a)

• b x a

• a x b

The maximum range of a gun on horizontal terrain is 16 km if g = 10 m/s². What must be the muzzle velocity of the shell?

• 200 m/s

• 100 m/s

• 400 m/s

• 300 m/s

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

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