NTA JEE Main 10th January 2019 Shift 1

In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

The density of a material in SI units is 128 kg m$$^{-3}$$. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is:

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

A block of mass $$m$$ is kept on a platform which starts from rest with a constant acceleration $$g/2$$ upwards, as shown in the figure. Work done by normal reaction on block in time $$t$$ is:

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms$$^{-1}$$, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is: ($$g = 10$$ ms$$^{-2}$$)

To mop-clean a floor, a cleaning machine presses a circular mop of radius $$R$$ vertically down with a total force $$F$$ and rotates it with a constant angular speed about its axis. If the force $$F$$ is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $$\mu$$, the torque, applied by the machine on the mop is:

A homogeneous solid cylindrical roller of radius $$R$$ and mass $$M$$ is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

A satellite is moving with a constant speed $$v$$ in circular orbit around the earth. An object of mass '$$m$$' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

Water flows into a large tank with flat bottom at the rate of $$10^{-4}$$ m$$^3$$s$$^{-1}$$. Water is also leaking out of a hole of area 1 cm$$^2$$ at its bottom. If the height of the water in the tank remains steady then this height is:

A heat source at $$T = 10^3$$ K is connected to another heat reservoir at $$T = 10^2$$ K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 W K$$^{-1}$$ m$$^{-1}$$, the energy flux through it in the steady-state is: