$A$ block of mass $M$ is placed on $a$ horizontal surface and it is tied with an inextensible string to $a$ block of mass, as shown in figure. A block of mass $m_0$ is also placed on $M$ In previous problem, the tension in the string will be
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A heavy box is to dragged along a rough horizontal floor. To do so, person $A$ pushes it at an angle $30^o$ from the horizontal and requires a minimum force $F_A$, while person $B$ pulls the box at an angle $60^o$ from the horizontal and needs minimum force $F_B$. If the coefficient of friction between the box and the floor is $\frac{{\sqrt 3 }}{5}$ , the ratio $\frac{{{F_A}}}{{{F_B}}}$ is
A lift is moving downwards with an acceleration equal to acceleration due to gravity. $A$ body of mass $M$ kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\mu $, then the frictional resistance offered by the body is
A curved in a level road has a radius $75\, m$. The maximum speed of a car turning this curved road can be $30 \,m / s$ without skidding. If radius of curved road is changed to $48\, m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........$m / s$.
Block $A$ of mass $30\, kg$ . is resting on a frictionless floor. Another block $B$ of mass $5\, kg$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.4$ while kinetic friction is $0.3$. If a horizontal force of $175\, N$ is applied to block $B$ , then the acceleration of the block $A$ will be ........ $m/s^2$ $(g = 10\, m/s^2 )$
A small object placed on a rotating horizontal turn table just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is
In the figure shown, a block of weight $10 \,N$ resting on a horizontal surface. The coefficient of static friction between the block and the surface ${\mu _s} = 0.4$. A force of $3.5\, N$ will keep the block in uniform motion, once it has been set in motion. A horizontal force of $3 \,N$ is applied to the block, then the block will
A plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be
A body of mass $2$ kg is moving on the ground comes to rest after some time. The coefficient of kinetic friction between the body and the ground is $0.2$. The retardation in the body is ...... $m/s^2$
A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The horizontal force $F$ applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu = Kx$ where $K$ is a $+$ ve constant. Then the tension at mid point of rod is