11.

A stationary body of mass m explodes into three parts having masses in the ratio 1 : 3 : 3. The two fractions with equal masses move at right angles to each other with a velocity of 1.5 ms^-1. Then the velocity of the third body is

• $4.5\sqrt{2} {\mathrm{ms}}^{-1}$

• 5 ms^-1

• $5\sqrt{32} {\mathrm{ms}}^{-1}$

• 1.5 ms^-1

A rocket of initial mass 1000 kg ejects mass at a constant rate of 10 kg/s with constant relative speed of 11 ms^-1. Neglecting gravity, the acceleration of the rocket 1 min after the blast is

• 11/40 ms^-2

• 22/40 ms^-2

• 1.1/40 ms^-2

• 1 ms^-2

An elastic ball is dropped from a height h and it rebounds many times from the floor. If the coefficient of restitution is e, the time interval between the second and the third impact, is

• ev/g

• e²v/g

• ${\mathrm{e}}^2\sqrt{\left(\frac{8\mathrm{h}}{\mathrm{g}}\right)}$

• ${\mathrm{e}}^2 \sqrt{\left(\frac{\mathrm{h}}{\mathrm{g}}\right)}$

An object of mass m is attached to light string which passess through a hollow tube. The object is set into rotation in a horizontal circle of radius, r₁. If the string is pulled shortening the radius to r₂, the ratio of new kinetic energy to the original kinetic energy is

• ${\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)}^2$

• ${\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2$

• $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}$

• $\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}$

Total angular momentum of a rotating body remains constant, if the net torque acting on the body is

• zero

• maximum

• minimum

• unity

A car is racing on a circular track of 180 m radius with a speed of 32 ms^-1. What should be the banking angle of the road to avoid changes of skidding of the Vehicle at this speed without taking into consideraion the friction between the tyre and the road ?

• 45°

• 60°

• 30°

• 15°

When a ceiling fan is switched on it makes 10 rotations in the first 3s. The number of rotations it makes in the next 3 s, assuming uniform angular acceleration is

• 40

• 30

• 20

• 10

A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to 1/3rd the escape velocity for that planet. The maximum height attained by the body is

• R/2

• R/3

• R/9

• R/8

A man weighs 80 kg on earth surface. The height above ground where he will weigh 40 kg, is : (radius of earth is 6400 km)

• 0.31 times r

• 0.41 times r

• 0.51 times r

• 0.61 times r

A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane. Then

• solid sphere reaches the ground first

• hollow sphere reaches the ground first

• both spheres reach the ground at the same time

• the time at which the spheres reach the ground cannot be specified by the given data