An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms$$-$$2].

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms$$-$$1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is : [use g = 9.8 ms$$-$$2]

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value of F applied, so that the block does not move upward, will be : (Given : g = 10 ms$$-$$2)

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

Three masses $$M=100\mathrm{kg},{\mathrm{m}}_1=10\mathrm{kg}$$ and $${\mathrm{m}}_2=20\mathrm{kg}$$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $$\mathrm{F}$$ is applied on the system so that the mass $${\mathrm{m}}_2$$ moves upward with an acceleration of $$2{\mathrm{ms}}^{-2}$$. The value of $$\mathrm{F}$$ is : ( Take $$\mathrm{g}=10{\mathrm{ms}}^{-2}$$ )

A monkey of mass $$50\mathrm{kg}$$ climbs on a rope which can withstand the tension (T) of $$350\mathrm{N}$$. If monkey initially climbs down with an acceleration of $$4\mathrm{m}/{\mathrm{s}}^2$$ and then climbs up with an acceleration of $$5\mathrm{m}/{\mathrm{s}}^2$$. Choose the correct option $$\left(g=10\mathrm{m}/{\mathrm{s}}^2\right)$$.

Two masses $$M_1$$ and $$M_2$$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $$M_2$$ is twice that of $$M_1$$, the acceleration of the system is $$a_1$$. When the mass $$M_2$$ is thrice that of $$M_1$$, the acceleration of the system is $$a_2$$. The ratio $$\frac{a_1}{a_2}$$ will be :

A bag is gently dropped on a conveyor belt moving at a speed of $$2\mathrm{m}/\mathrm{s}$$. The coefficient of friction between the conveyor belt and bag is $$0.4$$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion, is : [Take $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^{-2}$$ ]

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $$\theta$$. The magnitude of the contact force will be :

A block 'A' takes 2 s to slide down a frictionless incline of 30$${}^{\circ }$$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45$${}^{\circ }$$, the time taken by the block, to slide down the incline, will be approximately :

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length '$$\mathrm{L}-l$$' is hanging on the other side of the pully. At a certain point of time, when $$l=\frac{L}{x}$$, the acceleration of the chain is $$\frac{g}{2}$$. The value of x is __________.

Two bodies of masses $$m_1=5\mathrm{kg}$$ and $$m_2=3\mathrm{kg}$$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $${\mathrm{m}}_1$$ will be : [Take $$\mathrm{g}=10{\mathrm{ms}}^{-2}]$$

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be : (Assume the coil to be short circuited.)

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\varphi =(5t^3+4t^2+2t-5)$$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s$$-$$1. If the horizontal component of earth's magnetic field is 0.2 $$\times$$ 10$$-$$4 T, then emf induced between the two ends of the conductor is :

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire $$\mathrm{L}(\mathrm{L}>>l)$$. Both loops are coplanar and their centres coincide at point $$\mathrm{O}$$ as shown in figure. The mutual inductance of the system is :

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The ratio of {{{B_2}} \over {{B_1}}} is

A spherical shell of 1 kg mass and radius R is rolling with angular speed $$\omega$$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is {a \over 3} R2$$\omega$$. The value of a will be :

A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 2t where t is in second and $$\alpha$$ is in rads$$-$$2. At t = 0, the ball has angular velocity of 10 rads$$-$$1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :