A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms'.The kinetic energy of the other mass is

• 256 J

• 486 J

• 524 J

• 324 J

 A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force

• converts translational energy to rotational energy

• dissipates energy as heat

• decreases the rotational motion

• decreases the rotational and translational motion

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

• g' = 3g

• $\mathrm{g}\text{'} = \frac{\mathrm{g}}{9}$

• g' = 9g

• g' = 27g

If a vector$2 \hat{\mathrm{i}} + 3 \hat{\mathrm{j}} + 8 \hat{\mathrm{k}}$ is perpendicular to the vector $4 \hat{\mathrm{j}} - 4 \hat{\mathrm{i}} + \mathrm{\alpha } \hat{\mathrm{k}}$, then the value of α is

• -1

• $\frac{1}{2}$

• $-\frac{1}{2}$

• 1

A force F acting on an object varies with distance x as shown here. The force is in newton and distance is in metre. The work done by the force in moving the object from x = 0 to x = 6 m is

• 4.5 J

• 13.5 J

• 9.0

• 18.0 J

Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v₁ The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is 

• $\frac{\mathrm{a}}{\sqrt{{\mathrm{v}}^2 + {\mathrm{v}}_1^2}}$

• $\sqrt{\frac{{\mathrm{a}}^2}{{\mathrm{\nu }}^2 - {\mathrm{\nu }}_1^2}}$

• $\frac{\mathrm{a}}{\left(\mathrm{\nu } - {\mathrm{\nu }}_1\right)}$

• $\frac{\mathrm{a}}{\left(\mathrm{\nu } + {\mathrm{\nu }}_1\right)}$

A 5 A fuse wire can withstand a maximum power of 1 W in circuit. The resistance of the fuse wire is

• 0.2 Ω

• 5 Ω

• 0.4 Ω

• 0.04 Ω

If the angle between the vectors $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}} \mathrm{is} \mathrm{\theta }$, the value of the product $\left(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}\right). \overrightarrow{\mathrm{A}}$ is equal to

• ${\mathrm{BA}}^2 \mathrm{cos\theta }$

• BA² sinθ

• BA² sinθ cosθ

• zero

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

• $\frac{1}{2} {\mathrm{MR}}^2$

• MR²

• $\frac{7}{2} {\mathrm{MR}}^2$

• $\frac{3}{2} {\mathrm{MR}}^2$

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one-half of its maximum height. How high does the ball rise? ( Take, g = 10 m/s² )

• 15 m

• 10 m

• 20 m

• 5 m