The tension in the rope used to pull a body on an inclined surface remains constant at all the points, if and only if

The length of a metal wire is ${\ell }_1,$ when the tension in it is $T_1$ and is ${\ell }_2$ when the tension is $T_2.$ The natural length of the wire is:

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

A maximum of $3 \mathrm{N}$ force can be applied on a block, down the incline, that would still not move the block which is placed on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that does not move the block is $12 \mathrm{N}$. The coefficient of static friction between the block and the plane is $\left[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

Three forces of magnitude $6 \mathrm{N}, 6 \mathrm{N}$ and $\sqrt{72} \mathrm{N}$ act at a cormer of a cube along three edges of a cube, as shown in the figure. The resultant of the three forces is

Two equal forces are acting at a point, making an angle of $60°$ with each other. If their resultant force is equal to $40\sqrt{3} \mathrm{N},$ the magnitude of each force is $\underline{ }$

Two masses connected in series with two massless strings are hanging from a support as shown in the figure. Find the tension in the upper string

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $\left(f_a\right)$ cannot be ignored, the forces acting on the ball at the position $X$ are represented by

A rectangular frame of some mass has to be suspended symmetrically by two mass-less strings of equal length on two supports. It can be done in one of the three following ways as shown in below figures. The tension in the strings will be