Two masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in figure. The ratio of the tensions $T_1/T_2$ is
$\frac {M_1}{M_2}$
$\frac {M_2}{M_1}$
$\frac {(M_1+M_2)}{M_2}$
$\frac {M_1}{(M_1+M_2)}$
A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given ${m}=8 \,{kg}, {M}=16\, {kg}$
Assume all the surfaces shown in the figure to be frictionless.
A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is
A block of mass $m_1=1 \ kg$ another mass $m_2=2 \ kg$, are placed together (see figure) on an inclined plane with angle of inclination $\theta$. Various values of $\theta$ are given in List $I$. The coefficient of friction between the block $m _1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m _2$ and the plane are equal to $\mu=0.3$. In List $II$ expression for the friction on block $m _2$ given. Match the correct expression of the friction in List $II$ with the angles given in List $I$, and choose the correct option. The acceleration due to gravity is denoted by $g$.
[Useful information : $\tan \left(5.5^{\circ}\right) \approx 0.1 ; \tan \left(11.5^{\circ}\right) \approx 0.2 ; \tan \left(16.5^{\circ} \approx 0.3\right)$ ]
List $I$ | List $II$ |
$P.\quad$ $\theta=5^{\circ}$ | $1.\quad$ $m _2 g \sin \theta$ |
$Q.\quad$ $\theta=10^{\circ}$ | $2.\quad$ $\left(m_1+m_2\right) g \sin \theta$ |
$R.\quad$ $\theta=15^{\circ}$ | $3.\quad$ $\mu m _2 g \cos \theta$ |
$S.\quad$ $\theta=20^{\circ}$ | $4.\quad$ $\mu\left(m_1+m_2\right) g \cos \theta$ |
A monkey is decending from the branch of a tree with constant acceleration. If the breaking strength is $75 \%$ of the weight of the monkey, the minimum acceleration with which monkey can slide down without breaking the branch
A book of mass $5 \,kg$ is placed on a table and it is pressed by $10 \,N$ force then normal force exerted by the table on the book is ......... $N$