In an experiment the values of two spring constants were measured as $k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m}$ and $k_2=(20 \pm 0.3) \mathrm{N} / \mathrm{m}$. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

Consider a modified Bernoulli equation.

$$ \left(\mathrm{P}+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant } $$

If $t$ has the dimension of time then the dimensions of $A$ and $B$ are $\_\_\_\_$ , $\_\_\_\_$ respectively.

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^{\circ} \mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ} \mathrm{C}$, is $\_\_\_\_$ cm.

Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $L_A=2.5 \mathrm{~m}$ and $L_B=1.5 \mathrm{~m}$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1 / t_2$ is: