Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.

A body of mass $10\mathrm{kg}$ is moving with an initial speed of $20\mathrm{m}/\mathrm{s}$. The body stops after $5\mathrm{s}$ due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10{\mathrm{ms}}^{-2}$ )

A block of mass $$5\mathrm{kg}$$ is placed at rest on a table of rough surface. Now, if a force of $$30\mathrm{N}$$ is applied in the direction parallel to surface of the table, the block slides through a distance of $$50\mathrm{m}$$ in an interval of time $$10\mathrm{s}$$. Coefficient of kinetic friction is (given, $$g=10{\mathrm{ms}}^{-2}$$):

As shown in figure, a $$70\mathrm{kg}$$ garden roller is pushed with a force of $$\vec{F}=200\mathrm{N}$$ at an angle of $$30^{\circ }$$ with horizontal. The normal reaction on the roller is (Given $$\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$$)

A block of $\sqrt{3}\mathrm{kg}$ is attached to a string whose other end is attached to the wall. An unknown force $\mathrm{F}$ is applied so that the string makes an angle of $30^{\circ }$ with the wall. The tension $\mathrm{T}$ is: (Given $\mathrm{g}=10{\mathrm{ms}}^{-2}$ )

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

The time taken by an object to slide down 45$${}^{\circ }$$ rough inclined plane is n times as it takes to slide down a perfectly smooth 45$${}^{\circ }$$ incline plane. The coefficient of kinetic friction between the object and the incline plane is :

A block of mass $m$ slides down the plane inclined at angle $$30^{\circ }$$ with an acceleration $$\frac{g}{4}$$. The value of coefficient of kinetic friction will be:

Consider a block kept on an inclined plane (incline at 45$${}^{\circ }$$) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane($$\mu$$) is equal to :

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s$${}^2$$)

Given below are two statements : Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

The position vector of a particle related to time $t$ is given by $\vec{r}=\left(10t\hat{i}+15t^2\hat{j}+7\hat{k}\right)m$ The direction of net force experienced by the particle is :

Three forces $$F_1=10\mathrm{N},F_2=8\mathrm{N},{\mathrm{F}}_3=6\mathrm{N}$$ are acting on a particle of mass $$5\mathrm{kg}$$. The forces $${\mathrm{F}}_2$$ and $${\mathrm{F}}_3$$ are applied perpendicularly so that particle remains at rest. If the force $$F_1$$ is removed, then the acceleration of the particle is:

A body of mass $$500\mathrm{g}$$ moves along $$\mathrm{x}$$-axis such that it's velocity varies with displacement $$\mathrm{x}$$ according to the relation $$v=10\sqrt{x}\mathrm{m}/\mathrm{s}$$ the force acting on the body is:-

At any instant the velocity of a particle of mass $$500\mathrm{g}$$ is $$\left(2t\hat{i}+3t^2\hat{j}\right){\mathrm{ms}}^{-1}$$. If the force acting on the particle at $$t=1\mathrm{s}$$ is $$(\hat{i}+x\hat{j})\mathrm{N}$$. Then the value of $$x$$ will be:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed : A. By changing the magnitude of the magnetic field within the coil. B. By changing the area of coil within the magnetic field. C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

A square loop of area 25 cm$${}^2$$ has a resistance of 10 $$\Omega$$. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1.0 sec, will be

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$$R$$' is placed inside a large square loop of wire of side $$L$$ $$(L\gg R)$$. The loops are coplanar and their centres coincide :

A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be __________.