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A body of mass $40\,kg$ resting on rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{ s }=5, \mu_{ x }=0.4$, $g =10\,m / s ^2$ and the force $P$ is continuously applied on the body, then the acceleration of the body is $.........m/s^{2}$
Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction as $μ$. A force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards right
A body starts from rest on a long inclined plane of slope $45^o$ . The coefficient of friction between the body and the plane varies as $\mu = 0.3\,x$ . where $x$ is distance travelled down the plane. The body will have maximum speed ( for $g = 10\,m/s^2$ ) when $x=$ ........ $m$
A block of mass $m$ is placed on a surface having vertical cross section given by $y=x^2 / 4$. If coefficient of friction is $0.5$ , the maximum height above the ground at which block can be placed without slipping 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 .........$m / s$.
A $40 \,kg$ slab rests on a frictionless floor as shown in the figure. A $10 \,kg$ block rests on the top of the slab. The static coefficient of friction between the block and slab is $0.60$ while the kinetic friction is $0.40$. The $10\, kg$ block is acted upon by a horizontal force $100 \,N$. If $g = 9.8\,m/{s^2}$, the resulting acceleration of the slab will be ........ $m/s^2$
A block of mass $m$ is placed on a surface with a vertical coss section given by $y = \frac{{{x^3}}}{6}$ . If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is
An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is