A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be. respectively

A system consists of three masses m₁, m₂ and m₃ connected by a string passing over a pulley P. The mass $m_1$ hangs freely and m₂ and m₃ are on a rough horizontal table (the coefficient of friction=μ) The pulley is frictionless and of negligible mass. The downward acceleration of mass m₁, is (Assume,m₁=m₂=m₃=m)

A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?

The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of the plane is given by

A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is $45°$,the speed of the car is 

A car of mass m is moving on a level circular track of radius R. If ${\mathrm{\mu }}_{\mathrm{s}}$ represent the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0 \mathrm{m}/{\mathrm{s}}^2$. If $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$, the tension in the supporting cable is:

Two masses of 10 kg and 20 kg respectively are connected by massless spring as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown the 10 kg mass has acceleration 12 $\mathrm{m}/{\mathrm{s}}^2$. What is the acceleration of 20 kg mass?

The slope of a smooth banked horizontal surface road is $p$. If the radius of the curve be $r$, the maximum velocity with which a car can negotiate the curve is given by

The angle of banking at the turning of a road does not depend upon the

A block of mass m is in contact with the cart C as shown in the figure.

A gramophone record is revolving with an angular velocity $\omega .$ A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu .$ The coin will revolve with the record if: 

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, its acceleration is:

A body, under the action of a force $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k},$ acquires an acceleration of 1$m{s}^{-2}.$ The mass of this body must be

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is 

A particle of mass m is projected with velocity v making an angle of ${45}^{°}$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be 

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be 

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\mathrm{\theta }$ with the vertical

A pendulum bob is suspended in a Car moving horizontally with acceleration ‘a’ the angle the string will make with vertical is

A block of mass $m$ is placed on the floor of lift which is moving with velocity $v$ = $4t^2$, where $t$ is time in second and velocity  m/s. Find the time at which normal force on the block is three times of its weight.

A piece of wire is bent in the shape of a parabola y = $k{x}^2$ (y-axis vertical) with a

bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now  accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

A string with constant tension T is deflected through an angle $2{\theta }_0$ by a smooth fixed pulley. The force on the pulley is

$$\begin{gathered} \left(\mathrm{a}\right) 2\mathrm{T} {\mathrm{cos\theta }}_0 \\ \left(\mathrm{b}\right) \mathrm{T} {\mathrm{cos\theta }}_0 \\ \left(\mathrm{c}\right) 2\mathrm{T} {\mathrm{sin\theta }}_0 \\ \left(\mathrm{d}\right) \mathrm{T} {\mathrm{sin\theta }}_0 \end{gathered}$$

$$\begin{gathered} \mathrm{A} \mathrm{smooth} \mathrm{semicircular} \mathrm{wire} \mathrm{track} \mathrm{of} \mathrm{radius} \mathrm{R} \mathrm{is} \mathrm{fixed} \mathrm{in} \mathrm{a} \mathrm{vertical} \mathrm{plane} \mathrm{as} \mathrm{shown}. \\ \mathrm{One} \mathrm{end} \mathrm{of} \mathrm{a} \mathrm{light} \mathrm{springs} \mathrm{of} \mathrm{natural} \mathrm{length} \frac{3\mathrm{R}}{4} \mathrm{is} \mathrm{attached} \mathrm{to} \mathrm{the} \mathrm{lower} \mathrm{point} \mathrm{O} \\ \mathrm{of} \mathrm{the} \mathrm{wire} \mathrm{track}. \mathrm{A} \mathrm{small} \mathrm{bead} \mathrm{of} \mathrm{mass} \mathrm{m} \mathrm{which} \mathrm{can} \mathrm{slide} \mathrm{on} \mathrm{the} \mathrm{track}, \mathrm{is} \\ \mathrm{attached} \mathrm{to} \mathrm{makes} \mathrm{an} \mathrm{a} \mathrm{the} \mathrm{other} \mathrm{end} \mathrm{of} \mathrm{the} \mathrm{spring}. \mathrm{The} \mathrm{bead} \mathrm{is} \mathrm{held} \\ \mathrm{stationary} \mathrm{at} \mathrm{point} \mathrm{P} \mathrm{such} \mathrm{that} \mathrm{spring} \mathrm{makes} \mathrm{an} \mathrm{angle} \mathrm{of} 60° \mathrm{with} \mathrm{the} \mathrm{vertical}. \\ \mathrm{The} \mathrm{spring} \mathrm{constant} \mathrm{is} \mathrm{k} = \frac{\mathrm{mg}}{\mathrm{R}}. \mathrm{The} \mathrm{restoring} \mathrm{force} \mathrm{in} \mathrm{the} \mathrm{spring} \mathrm{at} \mathrm{that} \mathrm{instant} \\ \mathrm{is}- \\ \left(\mathrm{a}\right) \mathrm{mg} \\ \left(\mathrm{b}\right) \frac{1}{4}\mathrm{mg} \\ \left(\mathrm{c}\right) \frac{1}{8}\mathrm{mg} \\ \left(\mathrm{d}\right) \frac{1}{2}\mathrm{mg} \end{gathered}$$

Traffic is moving at 60 km/hr along a circular track of radius 0.2 km, the correct angle of banking is

In the figure pulley ${\mathrm{P}}_1$ is fixed and the pulley ${\mathrm{P}}_2$ is movable. If ${\mathrm{w}}_1={\mathrm{w}}_2$, what is the angle between ${\mathrm{AP}}_2{\mathrm{P}}_1$? (pulleys are frictionless)

A light spring is compressed and placed horizontally between a vertical fixed wall and a toy car-free to slide over a smooth horizontal table. If the system is released from rest, which graph best represents acceleration 'a' and distance 'x' covered by the car?

Find the acceleration of light pulley is 

A rigid ball of mass M strikes a rigid wall at ${60}^0$ and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be:
      

Which one of the following statements is incorrect?

A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\mathrm{\theta }$ for the block to remain stationary on the wedge is: