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A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.



If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

The one end of rope is passing over a frictionless pulley is tied with a block of weight, W as shown in figure. The co-efficient of friction between the block and the horizontal plane is $\mu$. If the other end is allowed to pull without sliding the block, the maximum pull is permitted as

A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plate. At the instant shown, edge QR is parallel to the x-axis and the body moves such that velocities of points P and R are $V_P$ and $V_R$ in the x and y directions, respectively. The magnitude of the angular velocity of the body is

A bullet of mass m travels at a very high velocity V (as shown in the figure) and gets embedded inside the block of mass M initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance s along the floor. Assuming $\mu$ to be the coefficient of kinetic friction between the block and the floor and g the acceleration due to gravity what is the velocity V of the bullet?

1. 212.5

A flexible but inextensible chain of length $l$ and weight $w$ N/m is held on a smooth table with an initial overhang 'a' as shown in figure. What will be the velocity $v$ with which the chain will leave the table if released?

The centre B of a wheel rolling on a plane surface moves with a speed $V_0$. The speed of point A, B and C are respectively

A simple pendulum of length of 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of $5\frac{m}{s}.$ The net force on bob at the mean position is

A stone of mass m at the end of a string of length I is whirled in a vertical circle at a constant speed. The tension is the string will be maximum when the stone is

A solid blcok 'A' weighting 'Q' kg is resting on a flat floor. A smooth cylindder 'B' weighting 'P' kg is placed between the solid A and the vertical wall as shown in figure. The friction between the cylinder, wall and the block A is negligible. The coefficient of friction between the block A and floor is $\mu$. The minimum weight P required to disturb the block A is

1. 5.5

A heavy block of mass m is slowly placed on a conveyor belt moving with speed v. If coefficient of friction between block and the belt is $\mu$, the block will slide on the belt through distance ____

A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel maas m. Symbol g represents the acceleration due to gravity.





The tension in the thread is

A particle is projected at an angle $\theta$ to the horizontal and it attains a maximum height H. The time taken by the projectile to the highest point, of its path is

A circular disk of a radius R rolls without slipping at a velocity V. The magnitude of the velocity at point P (see figure) is:

Two blocks with the mass M and m are in contact with each other and are resting on horizontal frictionless floor. When horizontal force is applied to the heavier, the blocks accelerate to the right. The force between the two blocks are.

The members carrying zero force (i.e. zero -force members) in truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e with no appreciable change in angles between the members), are

A simple mass-spring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t$, the equation of motion of the free vibration of the system is $m\ddot{z}+kz=0$. The natural frequency of the system is

A weight 'W' is supported by two cables as shown in the figure below. The tension in the cable making an angle $\theta$ will be the minimum when the value of $\theta$ is

An assembly made of a rigid arm $A-B-C$ at end $A$ and supported by an elastic rope $C-D$ at end $C$ is shown in the figure. The members may be assumed to be weightless at the lengths of the respective members as shown in the figure.







Under the action of concentrated load $P$ at $C$ as shown, the magnitude of tension developed in the rope is

A car is having weight W is moving in the direction as shown in the figure. The centre of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels, is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels $\left(R_f\right)$ and rear wheels $\left(R_r\right)$ are given by

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The wheel has a radius of $200mm$ and the wrap angle of the band is ${270}^{\circ }$. The braking force applied to the lever is limited to $100N$, and the coefficient of friction between the band and the wheel is $0.5$. No other information is given.

The maximum wheel torque that can be completely braked is

Two equal weight W and a single weight Q are attached to the ends, of a flexible but inextensible cord overhanging at a pulley as shown in figure, if the system moves with constant acceleration 'a'. What is the magnitude of the weight Q?

A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is

A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 seconds interval. The acceleration of the car is

A plane cantilever truss is loaded as shown in the figure. If a positive sign denotes tension and a negative sign compression, the axial force in the member 1 is

Two forces are acting on a point at an angle of $\alpha$ and $\beta$ as shown in figure. If the sum of these forces is 700 N directed vertically, What are the angles $\alpha$ and $\beta$?

For the truss shown in the figure, the forces $F_1$ and $F_2$ are 9 kN and 3 kN, respectively. The force (in kN) in the member QS is (All dimensions are in m)

Figure below shows a particle sliding on a frictionless track which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the end of track will the particle hit the ground? Assume, $g=10\frac{m}{s^2}$

A two member truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively

AB and CD are two uniform and identical bars of mass 10 kg each, as shown. The hinges at A and B are frictionless. The assembly is released from rest and motion occurs in the vertical plane. At the instant that the hinge B passes the point B', the angle between the two bars will be

A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel maas m. Symbol g represents the acceleration due to gravity.



The linear acceleration of the reel is

In a statically determinate plane truss, the number of joints (j) and the number of members (m) are related by

Two rigid bodies of mass $5kg$ and $4kg$ are at rest on a frictionless surface until acted upon by a force of $36N$ as shown in the figure. The contact force generated between the two bodies is

A system of particles in motion has mass center G as shown in the figure. The particle i has mass $m_i$ and its position with respect to a fixed point O is given by the position vector ${\rho }_i$. The position of the particle with respect to g is given by the vector ${\rho }_i$. The time rate of change of the angular momentum of the system of particles about G is (The quantity $\ddot{{\rho }_i}$ indicates second derivative of ${\rho }_i$ with respect to time and likewise for $r_i$

A particle of mass $m$ is suspended from a ceilling through a string of length $L$ the particle moves in a horizontal circle of radius r. what is the speed of the particle and the tension in the string for conical pendulum ?

The time variation of the position of a particle in rectilinear motion is given by $x=2t^3+t^2+2t.$ If v is the velocity and a the acceleration of the particle in consistent units, the motion started with

Tension in the cable supporting a lift of weight 'W' and having an acceleration of 'a' while upward is (g is acceleration due to gravity)

One end of a uniform rod of mass and length l is clamped end at a uniform angular velocity $\omega$. the force exerted by the clamp on the rod is

In a band brake the ratio of tight side band tension to the tension on the slack side is $3$. If the angle of overlap of band on the drum is ${180}^{\circ }$ the coefficient of friction required between drum and the band is

A rigid weightless platform $PQRS$ shown in the figure (not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by the weightless member $OJ$ and four weightless, frictionless rollers. Points $O$ and $J$ are pin connections. A block of $90kN$ rests on the platform as shown in the figure.





The magnitude of horizontal component of the reaction (in $kN$) at pin $O$, is

A shell is fired from a cannon. At the instant the shell is just 3 m/s, while the barrel is swimming upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

The figure below shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R. The tangential acceleration of the centre when the ball is at A is (neglect the radius of mass 'm')

A car moving with speed u can be stopped in minimum distance x when brakes are applied. If the speed becomes n times, the minimum distance over which the car can stopped would take the value

A mass 'M' is suspended from a ceiling through a string of length 'L'. This mass moves in a circle of horizontal radius 'r'. at constant speed such that it is a conical pendulum. The tension in the string will-be

As shown in figure, person A is standing at the centre of a rotating platform facing person B who is riding a bicycle, heading East. The relevant speeds and distances are shown in the given figure, a bicycle, heading East. At the instant under consideration, what is the apparent velocity of B as seen by A?

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The wheel has a radius of $200mm$ and the wrap angle of the band is ${270}^{\circ }$. The braking force applied to the lever is limited to $100N$, and the coefficient of friction between the band and the wheel is $0.5$. No other information is given.



The maximum tension that can be generated in the band during braking is

The rigid body shown in the fig. (a) has a mass of 10 kg. It rotates with a uniform angular velocity $\omega$. A balancing mass of 20 kg is attached as shown in fig.(b). The percentage increase in mass moment of inertia as a result of this addition is

A unifonn circular ring of mass M and radius r is rotating with an angular speed $\omega$ about an axis passing through its centre and perpendicular to the plane of the ring. Two identical beads, each of mass m, somehow get attached at two diametrically opposite points. The rotational speed of the ring will become