The fig shows a semo-cylinderical massless gate of unit length perpendicular to the plane of the page and is pivoted at the point `O` holding a stationary liquid of density `rho`. A horizontal foce `F` is applied at its lowest position to keep it stationary. The magnitude of the force is:

Figure shows a semi-cylindrical massless gate pivoted at the point O holding a stationary liquid of density rho . The length of the cylinder is l . Calculate, the horizontal force exerted by the liquid on the gate.

A light semi cylindrical gate of radius R is pivoted aat its mid point O, of radius R as shown in the figure holding liquid of density rho . The force F required to prevent the rotation of the gate is equal to

A light semi cylindrical gate of radius R is pivoted aat its mid point O, of radius R as shown in the figure holding liquid of density rho . The force F required to prevent the rotation of the gate is equal to

A square gate of size 4m x 4m is hinged at topmost point. A fluid of density rho fills the space left of it. The force which acting 1m from lowest point can hold the gate stationary is?

Two identical uniform thin rods have been connected at right angles to form a ‘T’ shape. One end of a rod is connected to the centre of the other rod. Length of each rod is L. The upside down ‘T’ can swing like a pendulum about a horizontal axis passing through the top end (see fig.). Axis is perpendicular to plane of the fig. The speed of the meeting point of the two rods is u = 2 sqrt(gL) when it is at its lowest position. Calculate the angular acceleration of the ‘T’ shaped object when it is at extreme position of its oscillation.

Two thin circular disks of mass 2kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. the axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of the motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x axis as the direction of motion of the truck and z-axis as the vertically upwards direction. if the truck has an acceleration of 9m//s^2 Calculate: (i) The force fo friction on each disk, (ii) The magnitude and the direction of the frictional torque acting on each disk about the centre of mass O of the object. Express the torque in the vector form in terms of unit vectors hati, hatj and hatk in the x,y, and z directions.

Two thin circular disks of mass 2kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. the axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of the motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x axis as the direction of motion of the truck and z-axis as the vertically upwards direction. if the truck has an acceleration of 9m//s^2 Calculate: (i) The force fo friction on each disk, (ii) The magnitude and the direction of the frictional torque acting on each disk about the centre of mass O of the object. Express the torque in the vector form in terms of unit vectors hati, hatj and hatk in the x,y, and z directions.