A light string passing over a smooth light fixed pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$g/8$$, then the ratio of masses is:

In the given arrangement of a doubly inclined plane two blocks of masses $$M$$ and $$m$$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $$m$$, for which $$M=10\mathrm{kg}$$ will move down with an acceleration of $$2\mathrm{m}/{\mathrm{s}}^2$$, is: (take $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$$ and $$\tan 37^{\circ }=3/4)$$

A block of mass $$m$$ is placed on a surface having vertical crossection given by $$y=x^2/4$$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

Three blocks $$A,B$$ and $$C$$ are pulled on a horizontal smooth surface by a force of $$80\mathrm{N}$$ as shown in figure The tensions T$${}_1$$ and T$${}_2$$ in the string are respectively :

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $$2\mathrm{kg}$$ is :

A $$1\mathrm{kg}$$ mass is suspended from the ceiling by a rope of length $$4\mathrm{m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45^{\circ }$$ with respect to the vertical axis as shown in figure. The magnitude of $$F$$ is : (Assume that the system is in equilibrium and $$g=10\mathrm{m}/{\mathrm{s}}^2$$)

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $$t$$. Which of the following curve best describes acceleration of the block with time :

A $$2\mathrm{kg}$$ brick begins to slide over a surface which is inclined at an angle of $$45^{\circ }$$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

A given object takes $$\mathrm{n}$$ times the time to slide down $$45^{\circ }$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45^{\circ }$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

A player caught a cricket ball of mass $$150\mathrm{g}$$ moving at a speed of $$20\mathrm{m}/\mathrm{s}$$. If the catching process is completed in $$0.1\mathrm{s}$$, the magnitude of force exerted by the ball on the hand of the player is:

A wooden block of mass $$5\mathrm{kg}$$ rests on a soft horizontal floor. When an iron cylinder of mass $$25\mathrm{kg}$$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $$0.1{\mathrm{ms}}^{-2}$$. The action force of the system on the floor is equal to :

A particle moves in $$x$$-$$y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i}\cos (\mathrm{kt})-\hat{j}\sin (\mathrm{kt})$$. If $$\mathrm{k}$$ is constant, the angle between $$\overrightarrow{\mathrm{F}}$$ and $$\overrightarrow{\mathrm{p}}$$ will be :

A heavy box of mass $$50\mathrm{kg}$$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A body of weight $$200\mathrm{N}$$ is suspended from a tree branch through a chain of mass $$10\mathrm{kg}$$. The branch pulls the chain by a force equal to (if $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$$) :

A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2($$ where $$m_2>m_1)$$. If the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, then the ratio of the masses $$\frac{m_1}{m_2}$$ is:

A transformer has an efficiency of $80 \%$ and works at $10\mathrm{V}$ and $4\mathrm{kW}$. If the secondary voltage is $240\mathrm{V}$, then the current in the secondary coil is :

A rectangular loop of length $$2.5\mathrm{m}$$ and width $$2\mathrm{m}$$ is placed at $$60^{\circ }$$ to a magnetic field of $$4\mathrm{T}$$. The loop is removed from the field in $$10\sec$$. The average emf induced in the loop during this time is

A coil is places perpendicular to a magnetic field of $$5000\mathrm{T}$$. When the field is changed to $$3000\mathrm{T}$$ in $$2\mathrm{s}$$, an induced emf of $$22\mathrm{V}$$ is produced in the coil. If the diameter of the coil is $$0.02\mathrm{m}$$, then the number of turns in the coil is: