11.

A body starts rolling down on an inclined plane, the top half of which is perfectly smooth and lower half is rough. The angle of the plane being 30°, if the body is brought to rest just when it reaches the bottom, then the ratio of force of friction and weight of the body is

• 1 : 1

• 1 : 2

• 2 : 1

• 3 : 2

A particle is projected upwards from the surface of the earth (of radius R) with a KE equal to half the minimum value needed for it to escape. To what height (h) does it rise above the surface of the earth

• R

• 2R

• $\frac{\mathrm{R}}{2}$

• (R)^1/2

In figure shown below, a particle is travelling counter clockwise in circle of radius 10 m. The acceleration vector indicated at a specific time. Find the value of 'v' at this time.

• 10 m/s

• 15 m/s

• 20 m/s

• 7 m/s

A lift of mass 1000 kg is descending with a speed of 6 ms^-1 . Suddenly the cable of the lift begins to slip and it falls with a constant acceleration a = $\frac{9}{6}$m / s² . What is the kinetic energy of the lift after falling a distance 15 m ?

• 121.3 kJ

• 155.6 kJ

• 147.4 kJ

• 134.1 kJ

A solid sphere rolls without slipping and presses a spring of spring constant k as shown in figure. Then, the compression in the spring will be

• $\sqrt{\frac{2\mathrm{M}}{3\mathrm{k}}}$

• $\sqrt{\frac{2\mathrm{M}}{5\mathrm{k}}}$

• $\sqrt{\frac{5\mathrm{k}}{7\mathrm{M}}}$

• $\sqrt{\frac{7\mathrm{m}}{5\mathrm{k}}}$

A pendulum made of a uniform wire of cross-sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T_m . If the Young's modulus of the material is Y, then $\frac{1}{\mathrm{Y}}$ is equal to

• $\left[{\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2 - 1\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

• $\left[{\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2 - 1\right]\frac{\mathrm{Mg}}{\mathrm{A}}$

• $\left[1 - {\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

• $\left[1 - {\left(\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{m}}}\right)}^2\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

Work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature ofthe gas increases by 7° C. The gas is (R = 8.3 J mol^-1 K^-1 )

• diatomic

• triatomic

• a mixture of monoatomic and diatomic

• monoatomic

Which of the following graphs represents resonance for low damping ?

• graph (1)

• graph (2)

• graph (3)

• None of these

A bat emitting an ultrasonic wave of frequency 2 x 10⁴ Hz flies at a speed of 6 m/s between two parallel walls. The beat frequency between the two frequencies heard
by the bat is (Given, speed of sound is 330 m/s)

• 600 Hz

• 800 Hz

• 900 Hz

• 1300 Hz

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases to V^q , where V is the volume of the gas. The value of q is $\left(\mathrm{where} \mathrm{\gamma } = \frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{V}}}\right)$

• $\frac{3\mathrm{\gamma } + 5}{6}$

• $\frac{3\mathrm{\gamma } - 5}{6}$

• $\frac{\mathrm{\gamma } + 1}{2}$

• $\frac{\mathrm{\gamma } - 1}{2}$