Laws of Motion

A$60HP$electric motor lifts an elevator having a maximum total load capacity of$2000kg.$If the frictional force on the elevator is$4000N,$the speed of the elevator at full load is close to :$(1HP=746W,g=10ms^{-2})$

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$,…

A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path…

A block of mass $2M$ is attached to a massless spring with spring-constant $k.$ This block is connected to two other blocks of masses $M$ and $2M$ using two massless pulleys and strings. The accelerations of the blocks…

The potential energy of a particle of mass m at a distance r from a fixed point O is given by $V(r)=kr^{2}/2$, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of…

Paragraph: A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis…

Paragraph: A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis…

A uniform wooden stick of mass 1.6 kg and length $l$ rests in an inclined manner on a smooth, vertical wall of height h $(<l)$ such that a small portion of the stick extends beyond the wall. The reaction force of the…

A block of mass $m_{1}=1kg$ another mass $m_{2}=2kg$ , are placed together (see figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in List I. The coefficient of…

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it…

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_{1}$…

Paragraph: A small block of mass $1 \mathrm{~kg}$ is released from rest at the top of a rough track. The track is a circular arc of radius $40 \mathrm{~m}$. The block slides along the track without toppling and a…