In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows

$\mathrm{P} = \frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\mathrm{cd}} \%$, Error in P is 

• 14 %

• 10 %

• 7 %

• 4 %

The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is

• − 2i − 3j

• − 2i + 3j

• 2i − 3j

• 2i + 3j

A stone falls freely under gravity. It covers distances h₁, h₂, and h₃, in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂, and h₃ is

• h₁ = 2h₂ = 3h₃

• ${\mathrm{h}}_1 = \frac{{\mathrm{h}}_2}{3} = \frac{{\mathrm{h}}_2}{5}$

• h₂ = 3h₁ and h₃ = 3h₂

• h₁ = h₂ = h₃

Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m ? (g is the acceleration due to gravity)

• Zero

• 2 mg

• 3 mg

• 6 mg

The upper half of an inclined plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

• $\mathrm{\mu } = \frac{1}{\tan \mathrm{\theta }}$

• $\mathrm{\mu } = \frac{2}{\tan \mathrm{\theta }}$

• µ = 2 tan θ

• µ = tan θ

A uniform force of (3i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i + k) m to position ( 4i + 3j - k) m. The work done by the force on the particle is

• 9 J

• 6 J

• 13 J

• 15 J

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2 kg moves with 8 ms^-1 speed. If the third part flies off with 4 ms^-1 speed, then its mass is

• 3 kg

• 5 kg

• 7 kg

• 17 kg

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

• $\frac{3\mathrm{g}}{2\mathrm{L}}$

• $\frac{\mathrm{g}}{\mathrm{L}}$

• $\frac{2\mathrm{g}}{\mathrm{L}}$

• $\frac{2\mathrm{g}}{3\mathrm{L}}$

9.

A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of $\frac{3{\mathrm{v}}^2}{4\mathrm{g}}$ with respect to the initial position. The object is

• ring

• solid sphere

• hollow sphere

• disc

A body of mass m taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

• mg2R

• $\frac{2}{3} \mathrm{mgR}$

• 3 mgR

• $\frac{1}{3} \mathrm{mgR}$